1

Incentives,Innovation,andImitation:SocialLearninginaNetworkedGroup

ThomasN.Wisdom

SubmittedtothefacultyoftheUniversityGraduateSchool

inpartialfulfillmentoftherequirements

forthedegree

DoctorofPhilosophy

intheDepartmentsofPsychologyandCognitiveScience,

IndianaUniversity

August2010

2

AcceptedbytheGraduateFaculty,IndianaUniversity,inpartialfulfillmentofthe

requirementsforthedegreeofDoctorofPhilosophy.

DoctoralCommittee

_________________________________________________

RobertL.Goldstone,Ph.D.

_________________________________________________

ElinorOstrom,Ph.D.

_________________________________________________

KevinE.Collins,J.D.

_________________________________________________

JasonGold,Ph.D.

_________________________________________________

EliotR.Smith,Ph.D.

3

Acknowledgements

IwouldverymuchliketothankRobGoldstone,LinOstrom,KevinCollins,EliotSmith,and

JasonGold for invaluable advice and assistance in shaping this research; ToddGureckis,

Michael Roberts, Drew Hendrickson, and everyone in the Percepts & Concepts Lab for

feedbackandadvice;AllenLee,AndyJones,ZoranRilak,XianfengSong,andSarahGrantfor

helping to program and design the experiments; and Frances Kidwell, Itai Hasak, and

BennisPavisianforassistancewithrunningtheexperiments.Thisworkwasfundedinpart

byanNSFIGERTtraineeship.

4

ThomasN.Wisdom

Incentives,Innovation,andImitation:SocialLearninginaNetworkedGroup

Humans’extraordinarytalentsforlearningfromtheirenvironmentsandfromeachother

arethebasisofculturalandtechnologicaldevelopment,butfactorsaffectingtheuseof

theseskillssuchastime,informationdifferences,groupsize,andmaterialincentivesare

notyetcompletelyunderstood.Weusedaseriesoflaboratoryexperimentstoinvestigate

thecauses,consequences,anddynamicsofsociallearningstrategiesemployedbygroupsof

peopleincomplexsearchenvironments,andhowindividualimitationandinnovation

behaviorsaffectresultsatthegrouplevel.Intheseexperiments,participantsplayeda

simplecomputer‐basedpuzzlegamewithothers,inwhichguesseswerecomposedofsets

ofdiscreteunitsthathadbothlinearandinteractiveeffectsonscore,andeachplayercould

viewandimitateentireguessesorpartsofguessesfromothersinthegroup.Players

receivedround‐basedscorefeedbackaboutthequalityoftheirownguesses,andinsome

cases,others'guesses.Ourresultsshowedthatparticipantsusedseveralsociallearning

strategiespreviouslystudiedinotherspecies,aswellasstrategiesstudiedinthecontextof

innovationdiffusion,suchasimitationbiasestowardsolutionssimilartoone’sown,and

towardincreasinglypopularsolutions.Wefoundthattheriskofexploringinalargeand

complexproblemspacecausedparticipantstotakeaconservativeapproach,withsmall

amountsofinnovationandimitationusedtoacquiregoodsolutionsandmakeincremental

changesinthesearchforbetterones.Finally,wefoundthatimitation,ratherthanmerely

beingusedtocopyothersandavoidexploration,wasoftenusedbygroupmembersto

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improveoneachothers’guesses.Contextualfactorsthatdisruptedordiscouraged

imitationgenerallyresultedinpooreroutcomesfortheentiregroup,becauseofareduced

capacityforparticipantstocreatesuchcumulativeimprovements.Theseresultsare

discussedinthecontextofknowledgeasacommons,withimplicationsforthepromotion

ofinnovationsandintellectualpropertypolicy.

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TableofContents

1.(A)socialLearning...............................................................................................................................................7

2.Experiment1–PictureGame......................................................................................................................29

3.Experiment2–CreatureGameA...............................................................................................................53

4.ExplorationasaSocialDilemma................................................................................................................89

5.Experiment3–CreatureGameB(scorevisibility).........................................................................101

6.KnowledgeasProperty................................................................................................................................129

7.Experiment4–CreatureGameC(paymentandprotection)......................................................145

8.GeneralDiscussion.........................................................................................................................................188

References...............................................................................................................................................................195

7

1.(A)socialLearning

1.1.Introduction

Penguinsarethoughttobewarm‐bloodedanimalslikeotherbirds,butanoften‐told

talesuggestsotherwise.Asthestorygoes,agroupofpenguinswilloftenhesitatebefore

leavingtheicetoforageforkrill,becausealeopardsealmaybewaitinginthewaterto

forageforthem.Eachpenguinwouldprefertofindkrillassoonaspossibleandnevermeet

aleopardseal,buttheonlywaytobesurethewaterisfineisforatleastoneofthemto

jumpin.Thepenguins'simplesolutiontothisdilemmaistopushoneoftheirfellowsover

theedgeandobserveitforsignsofbeingdevoured(Dawson,1974).

Thankfully,humansocietieshavedevelopedinsuchawaythatgoingouttofind

fooddoesnottypicallyrequirenudgingourneighborsintothejawsofahungrypredator.

Butwedodependheavilyoninformationabouttheexperiencesofothersthatweexpectto

shareinsomeform.Infact,therearefewactivitiesthathumansparticipateinthatdonot

dependinsomewayonknowledgeobtainedfromothers.Thisisevidentuponcasual

reflectionabouthowpeoplegatherinformationandmakechoicesaboutthingslike

restaurantsormovies,candidatesforajoborpoliticaloffice,anewcitytoliveinoralarge

householdpurchase.Such"sociallearning"allowspeopletoobtaininformationabout

availableoptionswithoutundertakingthecostlyprocessofdirectlyevaluatingeachone,

thoughwithouttheincreasedaccuracythatsuchevaluationmightprovide.Thisprompts

thequestionofhowdecisionsaremadebetweentheoptionsoflearningaboutthe

environmentdirectlythroughexperience,orindirectlyviainformationprovidedbyothers.

Learningdirectlyfromtheenvironmentoftencarriesacostforthelearnerinterms

ofriskorresources,sowhenpossible,peoplewilloftenprefertoobtaininformation

8

indirectlythroughotherswithoutindividuallybearingthecostoflearningonone’sown.If

toomanypeopleavoidthecostsofdirectindividuallearningbutcontinuetomakeuseof

theinformationavailablethroughindirectsociallearning,anundesiredstagnationor

reducedadaptationtocomplexityandchangeintheenvironmentmayresult.

Ontheotherhand,whenlearnersareincompetitionforresources,eachlearner

mayhaveanincentivetopreventimitationbyothersoftheircostly,individually‐obtained

information.Adifferentproblemmayresultfromthisavoidanceofinformationsharing,

becauselearnersarepreventedfrombuildinguponandimprovingothers'solutions,which

canleadtorepeated"reinventionofthewheel,"anotherkindofstagnation.Ifanindividual

canpreventotherindividualsfromimitatingtheirsolutions,thenthecollectivebenefitsof

theirinnovationswillbeunderutilized.

Thesetradeoffsbetweenshort‐termself‐interestandgroupinterestcanbetreated

asanexampleofthewell‐studiedclassofphenomenaknownassocialdilemmas.Such

dilemmasapplytouseofnaturalresourcessuchasfisheries(Acheson,Wilson,&Steneck,

1998)aswellasartificialresourcessuchasirrigationsystems(Siy,1982).Alarge

literatureoftheory,fieldresearchandlaboratoryexperimentationhasbeenbuiltaround

thestudyofsocialdilemmas,andtheenvironmentalandinstitutionalfactorsthatcan

contributetotheirsolutions(Ostrom,1990).Recently,themethodsandframeworksused

toanalyzesocialdilemmasofphysicalresourceshavebeenproductivelybroughttobear

onthequestionofknowledgeasaresource(Hess&Ostrom,2007).

Thoughnotalwaysformallytreatedassuch,thesocialdilemmasofsociallearning

areaddressedinthepoliticaleconomyofknowledgeasatradablecommodity,intheform

ofintellectualproperty(IP).Intheory,IPlawandpolicyattempttobalancetheinterestsof

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knowledgecreatorsandusersinordertofurthertheprogressofknowledge,giventheir

environmentsandincentives.However,thedistinctionbetweenknowledgecreatorsand

usersisnotalwaysclear,becauseknowledgecanbeusedasafoundationorscaffoldingfor

creatingfurtherknowledge.Sorestrictivepropertyrightsgrantedtoincentivizeknowledge

creatorscanactuallyhavetheeffectofimpedingtheprocessofcreation,reducingbenefits

forall.Thusadilemmaarisesintheconflictbetweentheprivateinterestsofindividuals

andthecollectiveinterestsoftheirgroupsintheuseofcurrentknowledgeandthecreation

offutureknowledge.

Thecomplexityofreal‐worldlearninganddecisionmakingmakesitdifficultto

teaseaparttheeffectsoffactorssuchasindividualdifferences,groupinfluence,and

environmentalcharacteristics,aswellaschangesinlearningandinteractionsovertime.

Theseriesofexperimentsreportedinthisdissertationwillattempttobridgetheindividual

andgroupperspectives,byexploringthedynamicinterrelationshipsofactions,incentives,

andinstitutionsinvolvedintheexchangeofideas,andtheirconsequencesforboth

individualsandgroups,throughaseriesofcontrolledlaboratoryexperimentsonhumans.

1.2.(A)sociallearning:Definitionsandbackground

BoydandRicherson(2005)defined"sociallearning"as"theacquisitionofbehavior

byobservationorteachingfromotherconspecifics."Sociallearninghasbeenstudied

extensivelyinhumans(e.g.Hurley&Chater,2005),aswellasnon‐humananimals,

includingforagingchoicesinstarlings(Templeton&Giraldeau,1996),foodpreferencesin

variousrodentspecies(Galef&Giraldeau,2001),andmatechoicesinblackgrouse

(Höglund,Alatalo,Gibson,&Lundberg,1995)."Asociallearning"canbedefinedconversely

10

astheacquisitionofbehaviorbyindividualinnovationorexplorationoftheenvironment,

withoutrecoursetoinformationfromothers.

Laterinthispaper,"asociallearning"and"innovation"willbeusedinterchangeably,

aswill"sociallearning"and"imitation."However,agreatdealofresearchhasgoneinto

attemptingtodefineanddisambiguatethevarietiesoflearningthatorganismsexhibit.

Beforewegoon,wewillsurveysomeofthisresearchandclarifywhichareaswewillbe

exploringindetail,andwhatwewillbeneglectinginordertoachievethisfocus.

1.2.1.Sociallearning/imitation

Galef(1988)reviewedmanystudiesofsociallearninginvariousspeciesinan

attempttoclarifythedefinitionsandexplanationsthathavebeenusedforthese

phenomena.Galefnotedinhisreviewthefutilityofusingtheword"imitation"inageneral

andunambiguousway,becauseoftheoverabundanceofusesanddefinitionsithas

acquiredovertheyears.Galefdiscussesthisabundancebeginninginthemodernerawith

Romanes(1884),Morgan(1900),andThorndike(1911),whosedifferenceswererootedin

differingviewsabouttheevolutionofhumans,andtheevidenceofprecursorsofhuman

abilitiesinotheranimals.

SimilarlytoBoydandRicherson(2005),Box(1984)suggested"sociallearning"asa

genericdescriptiveterm,todistinguishsocially‐influencedlearningfromlearningthatis

notinfluencedbyothers,thoughGalef(1988)notesthatthisdistinctionisnotnecessarily

clear,since"itisalwaystheindividualwholearns;"behaviorsmaybeinitiallyacquired

fromothersbutsubsequentlymaintainedbyindividuallearningoffavorableconsequences.

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Wedonotintendtoattempttoresolvethisambiguity;itmustremaininthebackgroundto

helpexplainlearningbehaviorsinanyparticularcontextasamixtureofinfluences.

Itisimportanttodistinguishbetweentwomajordescriptivetermsforsocial

influence:(1)"socialenhancement,"inwhichothersinfluencetheperformanceof

behaviorsalreadyestablishedinanindividual'srepertoire(Galef,1988);and(2)"social

transmission,"inwhichsocialinteractionincreasesthelikelihoodthatanindividualwill

cometoindependentlyperformabehaviorinitiallyintherepertoireofanother,suchthat

thereisan"increasedhomogeneityofbehaviorofinteractantsthatextendsbeyondthe

periodoftheirinteraction"(Galef,1976).Forexample,inthemid‐20thcenturywhenitwas

commonformilktobedeliveredandleftoutsideofhomes,itwasnoticedthatincreasing

numbersofbirdswerelearningtoopenmilkbottlestodrinkthecreamfromthetop

(Fisher&Hinde,1949).Thiswasfoundtobeacaseofsocialenhancementratherthan

socialtransmission:laterexperimentsshowedthatforthepurposesoflearninghowto

opencontainers,allowingnaïveindividualstofeedfromcontainersopenedbyotherswas

justaseffectiveasallowingthemtoobserveaconspecificopeningacontainer.So

conspecifics'actvitiesfocusedothers'subsequentforagingonsimilarcontainers,whose

topswerevulnerabletoexistingfeedingbehaviorssuchaspecking(Sherry&Galef,1984,

1990).

Thephenomenathatthispaperwillexaminegenerallyfallunderthedescriptionof

"socialtransmission"ratherthan"socialenhancement;"weareinterestedinthespreadof

locallynovelinformationviapeerobservation,ratherthantheinfluenceofsocial

interactiononuseofinformationpossessedbyallgroupmembers.

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Alargevarietyofexplanatoryterminologyhasdevelopedtorefertotheorized

behavioralmechanismsthatcouldunderlietheabovedescriptiveterms.Thiscollectionof

terminology,accordingtoGalef(1988),is"extensive,contradictory,andvague",and

thoughithasnotprovedadequateforexhaustivelyclassifyingoreffectivelyexplaining

sociallearningbehavior,ithasbeenhelpfulinsuggestingapproachesforexperimental

analysisofthemyriadwaysinwhichsocialinteractioninfluencesbehavior.Followingare

severalofthemorewidely‐usedtermsinthisarea.

"Stimulusenhancement"(Spence,1937)and"localenhancement"(Thorpe,1963)

refertosituationsinwhichobservationofademonstrator'sactions,orevidencethereofin

theenvironment,causetheobservertodirectagreaterproportionofitsbehaviortoward

thelocationorobjectofthedemonstrator’sactivity."Socialfacilitation"referstosituations

inwhichthepresenceofothers"energizesallresponsesmadesalientbythestimulus

situationconfrontingtheindividualatthemoment"(Zajonc,1965)."Contagiousbehavior"

isusedforsituationsinwhich"theperformanceofamoreorlessinstinctivepatternof

behaviorbyonewilltendtoactasareleaserforthesamebehaviorinothersandsoinitiate

thesamelineofactioninthewholegroup,"suchasyawninginhumans(Thorpe,1963).

"Copying"referstosituationsinwhichanobserverissensitivetothedegreeofsimilarity

betweenitsownbehavioranditsmodel's,anditsresponsesarereinforcedpositivelywith

greatersimilarityandnegativelywithdissimilarity(Miller&Dollard,1941;Thorndike,

1911).

"True"or"reflective"imitation,alsoknownas"observationallearning,"requires

thattheperformanceofanactissufficientlyinstigatedsimplybyobservingit,andinvolves

purposeful,goal‐directedcopying(Galef,1988).Bandura(1965)calledhumans'raretalent

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forsuchimitation"no‐triallearning,"becauseitisevenfasterthantheone‐triallearning

observedinanimalswithastrongbuilt‐intendencytoformcertainassociations(e.g.

betweenthetasteofafoodandasubsequentstomachache).Evidencefor"true"imitation

inotheranimalshassofarbeenunconvincing(Davis,1973;Hall,1963)becauseofthe

difficultyofcontrollingforallofthealternativesociallearningprocesses(Galef,1988;

Heyes,1993).

Thisdissertationisconcernedmainlywithphenomenathatfallunderthe

descriptionof"socialtransmission,"sooftheaboveexplanatoryterms,wewillbelooking

mainlyto"true"imitation.Theexperimentsdescribedhereinwillbedesignedsuchthat

participantsaregivensufficientinformation,ability,andopportunitytopurposefully

observeandimitateothers.Theseaspectswillbeexplainedinmoredetailinlatersections.

1.2.2.Asociallearning/innovation

Asmentionedabove,ouruseoftheterm"asociallearning"isessentiallydefined

negativelyastheprocessofobtainingorgeneratinginformationfromsourcesotherthan

one'sfellowlearners.Theterm"innovation"isusedasashorthandoutoftheneedfora

conciseandfamiliardescriptorfortheimpliedindividualintroductionofinformationthat

islocallynovel(givenaverylargespaceofoptionstoexplore)amongagroupoflearners,

asopposedtothetransmissionofexistinginformationbetweenlearners.Using

"innovation"inthiswayinvolvessomeriskofconfusion,however,becausethistermisalso

usedheavilyinthebroaderstudyofcreativityanditsinstantiationinscientific,industrial,

andartisticpractice.(SeeSternberg(1999),KouniosandBeeman(2009),Paletzand

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Schunn(2010),Dunbar(1999),andGarciaandCalantone(2002)forhintsastothebreadth

ofthisfield.)

Intheinterestofbrevity,thecomplexityandspecificityofanalysisinthisliterature

willbeomitted.Wewilltrytoretainsomeclaritybylimitingourdefinitionofinnovationto

theuseoflocallynovelsolutionelementsbyindividualsamplingfromtheenvironmentina

problem‐solvingcontext,asopposedtoobtaininglocallyknownsolutionelementsthrough

observationofothers.

1.3.Learningstrategiesandtradeoffs

GabrielTarde,oneoftheforefathersofsocialpsychology,consideredinnovation

andimitationtobe"thefundamentalsocialacts"(Tarde1903/1969).Innovation

(generatinglocallynovelapproachestosolvingproblems)producesadiversityof

solutions,thoughoftenatacostinresources(suchastimeorenergy)orrisk(ingivingup

theopportunitytoexploitmorereliablesolutionsinfavorofsomethingneworunknown).

Imitationallowsadecisionmakertoemploysolutionsdiscoveredandpassedonbyothers

withouthavingtodevelopthemindependentlyusingcostlytrial‐and‐errorlearning.When

adecisionmakeracquiresinformationfromothersaboutpossiblesolutionstoaproblem,

theresourcesnotexpendedininformationgatheringcanbeusedforotheraspectsof

problemsolving,thusimprovingperformanceoverall.

Ofcourse,dominationofacommunitybyeitherinnovationorimitationcanbe

problematic.Excessiveinnovationisunhelpfulbecausegoodideasarenotpropagatedand

extendedbyothers.Excessiveimitationismaladaptivebecausegoodbutsuboptimal

solutionsarespreadtotheexclusionofbetteralternativesthatareleftunexplored.A

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commonassumptionisthatthecollectivecostsofexcessiveimitationwithinagroupare

particularlydetrimental–therearetypicallystrongincentivesforindividualstopursue

largelyimitativestrategiestoavoidrisk,whichmayleadtoadearthofgoodnewsolutions

thatwouldbenefiteveryoneinthegroup.Sothegroupmaybebetteroffifimitationisnot

universallychosen,buteachindividualisbetteroffbychoosingimitation.Thisideahas

strongparallelsinthelargebodyofresearchonsocialdilemmas,inwhichindividuals’self‐

interestsareinconflictwiththesharedinterestsofthemselvesandothersfacingthesame

problem.Researchonsocialdilemmashasconsistentlyshownthatwhensuchinteractions

arerepeatedovertime,andparticipantsareabletorecognizethedilemmatheysharewith

others,theyareoftenabletoadapttheirbehaviortoameliorateoravoidsocialdilemmas

(Ostrom,1990).

Laland(2004)reviewedstudiesofanimal(includinghuman)sociallearning

strategies,andtheirinteractionswithasociallearninginvariousfoodforagingbehaviors,

aswellasmatechoice,foodpreferences,andotherimportantdecisions.Ingeneral,itwas

foundthatthedefaultstrategy(thatis,thepreferredoptionwheneveravailable)isthe

simplestpossiblebehavior:exploitationofanexistingsolutionorknownresource

continuesuntilitisnolongerproductive,atwhichpointeitherinnovationorimitationcan

beusedtoacquireanewsolution.Mostofthestrategiesstudiedformakingsuchdecisions

canbedividedinto“when”and“who”strategies;thatis,heuristicsthatdictateunderwhat

circumstancessociallearningisfavoredoverasociallearning,and,whenitisfavored,those

thatdeterminefromwhichothersanindividualwilllearn.

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1.3.1.Whentoimitate:Costlyinformation

Decidingwhentousesociallearningoftendependsonarelativeassessmentof

asociallearningasanalternative.Often,thereisgreaterrelianceonsociallearningwhen

acquiringinformationthroughasociallearningiscostly(Boyd&Richerson,1985).These

costscanbeintheformoftheresourcesrequiredtocarryoutasociallearning,theriskof

acquiringinformationthatwillnotbereliableinthefuture,andtheriskassociatedwith

learningabouthazardsdirectly(e.g.predators).Asmightbeexpected,sociallearningabout

predatorshasevolvedinawidevarietyofanimals(Mineka&Cook,1988).Returningtothe

AdeliepenguinsmentionedatthebeginningofChapter1,itisdifficulttoprovethatthey

intentionallypushoneanotherintothewatertotestforleopardseals(ratherthan

accidentallyjostlingoneanotherofftheedge),buttheydoavoidthewatertemporarily

whenoneoftheirfellowsiseaten(Dawson,1974).Ithasalsobeenshownthattheyare

sensitivetotheeffectsofpredatorsongroupsize:theyarelesslikelytoenterthewaterifa

groupreturningfromaforagingrunisunusuallysmall,indicatingthatithasbeenattacked

anddispersedbyaleopardseal(Müller‐Schwarze,1984).Perhapsmoresurprisingisthe

factthatpredatoravoidancelearninghasevolvedinsomecasesbetweendifferentspecies

vulnerabletothesamepredators(Mathis,Chivers,&Smith,1996).Thisstrategyis

beneficialbecauseitallowsminimalindividualcontactwithhazards,thoughifone

individuallearnsthe“wrong”hazards,imitationbyothersmaybeinefficientordangerous.

Arelatedstrategyistorelyonsociallearningwhenataskisdifficulttolearn

asocially.Suchastrategyhasbeenobservedintheprocessingoffoodswithphysicaland

chemicaldefensesbygorillas(Byrne&Russon,1998)andinanexperimentalvisual

identificationtaskinhumans(Baron,Vandello,&Brunsman,1996).Again,thisstrategycan

17

savevaluableriskandeffortforimitators,butiftheexamplestheylearnfromareflawed,

inefficientorharmfulbehaviorscanspreadinagroup.

1.3.2.Whentoimitate:Resolvinguncertainty

Another"when"strategyistocopyotherswhenoneisuncertainabouttherelative

valueofavailableoptions.Forinstance,BeckandGalef(1989)showedthatwhen

presentedwithtwonovelfoods,ratsshowedabiasfortheonethathadbeenconsumedby

conspecifics,asevidencedbytheodorontheirbreath;whenthefoodswerefamiliar,this

biaswasmuchweaker.Suchstrategiesareespeciallyusefulwhen,asabove,informationis

costlytogatherasocially–samplingfoodswithoutregardtoothers’decisionscanresultin

insufficientnutritionorevenpoisoning.

Anearlystudyofsocialinfluenceinhumansfoundthatinasimpleperceptualtask,

thelesscertainanindividualwasofhisownjudgment,themorelikelyhewastobe

susceptibletotheinfluenceofothers(Deutsch&Gerard,1955).Likewise,whenan

individualisuncertainabouttheappropriateresponseinaparticularsituation(becauseof

eitheralackofinformationorthefailureofpreviousresponses),itismorelikelythatthe

individualwillresorttoimitation(Thelen,Dollinger,&Kirkland,1979).Whilerandomly

tryingoutsocialbehaviorsisnotusuallypoisonous,socialmistakes(violationsofnorms)

canresultinostracism,whichhasbeenshowntocauseneurologicalresponsessimilarto

thoseofphysicalpain(Eisenberger&Lieberman,2004).Thisisthoughttobeduetothe

evolutionarynecessityofgroupinclusionforsurvival(MacDonald&Leary,2005).

However,ifnormsareharmful,theircostsmayoutweighthebenefitsofinclusioninthe

group.

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1.3.3.Benefitsofimitationdependonselectivity

Itmaybethatonceadecisionismadetoimitateothersviaoneofthestrategies

above,individualsdonotmindwhotheycopy,aslongastheyavoidthecostsofasocial

learning.However,asimulationbyRogers(1988)ofagentsinanonstationary

environmentshowedthatifavoidanceoflearningcostsistheonlybenefitofimitation,then

theadditionofagentswhopersistentlyimitate(andchoosetargetsofimitationrandomly)

toapopulationofindividuallearnersdoesnotimprovetheaveragefitnessofthe

population.Thisisbecauseovertime,thecostsavoidedthroughimitationwillbebalanced

bycostsresultingfromtheuseofinformationthatisnolongeraccurate.Thusat

equilibrium,amixedpopulationofsocialandasociallearnershasthesameaveragefitness

asanasocial‐onlypopulation.(Asimilarconclusionwasreachedinatheoreticalanalysisof

foragingbehaviorbyGiraldeau,Valone,&Templeton(2002).)

BoydandRicherson(1995)andKamedaandNakanishi(2002)confirmedthese

results,butalsoextendedthemtoshowthatwhensociallearnerscanimitateselectively

(e.g.imitatingwhenindividualexplorationisrelativelyunreliableandthusmorecostly),

theoverallfitnessofthepopulationcanincrease,becausebothindividualandsocial

learningcanbecomemoreaccurate.

1.3.4.Whotoimitate:Frequency‐biasedstrategies

Frequency‐dependentimitationtakesintoaccounttherelativeprevalenceof

behaviorswhendecidingwhichtoimitate.Thisoftenentailsconformitytothebehavior

commontothegreatestnumberofobservedmodels.Suchbehaviorhasbeenobservedin

19

manyspecies,includingguppies(Lachlan,Crooks,&Laland1998),rats(Beck&Galef,

1989),andhumans(Hurley&Chater,2005).Granovetter's(1978)theoryofinnovation

diffusionisbasedona"threshold"proportionofgroupmembersnecessaryforan

individualtoadoptaninnovation.Suchconformitycanresultfromagoalofobtaining

informationabouttheutilityofasolutionfromitsapparentpopularity(informational

conformity),oravoidingtheappearanceofdeviancefromagroupanditsnorms

(normativeconformity).

1.3.5.Whotoimitate:Payoff‐biasedstrategies

Manyselectivestrategiesinvolveobservingthesuccessofmodelsinorderto

determinewhichtoimitate.Such"payoff‐biased"strategiescanuseanyofseveralcriteria,

dependingontheinformationaboutothers'successthatisavailable.Anindividualcan

simplyimitateany“successful”individual(whichrequiresonlysomeminimalthresholdor

criteriaforsuccess),ashasbeenshowninunsuccessfulbats'tendencytofollowpreviously

successfulbatstofeedingsites(Wilkinson,1992).Addingabitofcomplexity,onemight

comparethepayoffsofallindividualsandcopythemostsuccessful,asassumedinmany

theoreticalmodelsofhumandecisionmaking(Schlag,1998).Anindividualmayalso

imitateanydemonstratormoresuccessfulthanitself(whichrequiresevaluationof,and

comparisonbetween,theindividual'sownperformanceandthedemonstrator's).

Whilesuchstrategiesmayallowanimitatorgreatercertaintyinthepayoffofa

particularchoice,theymayalsorequiregreateffortininformation‐gatheringand

calculation,andtheserequirementsmaygrowexponentiallywiththesizeofasocialgroup

andtheirresponsivenesstoeachother.Thefeasibilityofsuchstrategiesisquestionedin

20

theoriesofboundedrationality,whichposit"fastandfrugal"heuristicsthatallowdecision

makerstoprosperwithlimitedinformationandcomputationalresources(Gigerenzer&

Goldstein,1996).Inpractice,suchlimitationsmaysubstantiallychangethecost‐benefit

calculationforcomplicatedstrategies,andleaddecisionmakerstofallbackonsimpler

strategiesorfacereducedperformanceinthefaceofexcessinformationprocessing

requirements.HeiseandMiller(1951)showedthatinadifficultcommunicationtask,the

removalofsomeparticipantcommunicationcapacityledtoincreasedperformance.The

broaderphenomenonofreducedperformanceinthepresenceoflargeamountsof

informationhasbecomeknownas"cognitiveoverload"(Sweller,1988).

Thoughmanymodelssuggestthatcopyingsuccessfulindividualscanbeaneffective

strategy,thebehaviorresponsibleforsuccessmaynotbeapparent,andthusunproductive

ormaladaptivebehaviorsmayaccompanysuccessfulones(Boyd&Richerson,1985).Even

ifaccurateinformationaboutagoodsolutionisavailable,itsuseorexploitationbytoo

manyusersmayreducethebenefitsavailabletoeach.Thussimplepayoff‐biasedstrategies

mayhavecostsintheformofcrowdingandoveruse,whicharenotremediableinthelong

runwithoutmorecomplexcontingentstrategiesthatrecognizetheeffectsthatotherusers

haveonthepayoffofsomesolutions.

1.4.Conformityandculture

Researchonhumansociallearningisfairlywidelydispersedacrossavarietyoffocal

behaviorsandmethodologies,whichisunderstandablegiventhemyriadpossiblefunctions

forsocially‐mediatedinformationinsuchasociallycomplexorganism.Belowisafocused

summaryofsomeofthisresearch.

21

1.4.1.Innovationdiffusion

Inhisstudiesofthediffusionofinnovationsacrosspopulations,Rogers(2003)

positsseveralfeaturesofaninnovationthatcanaffectitsadoption,amongthemthe

relativeadvantageobtainedbyreplacingaprevioussolutionwiththeadoptedinnovation,

andthecompatibilityoftheinnovationwithprevioussolutions.Theformerisaclear

analogtothesimplepayoff‐biasedimitationstrategiesmentionedabove,butthelatter

dealswithmorecomplexcostsofadoption.“Backwardcompatibility”withaprevious

solutionmaybedesiredtominimizethecostsofadaptationbytheadopter,suchas

learninghowtouseit,orreplacingitemsusedcomplementarilywithit.Compatibilitymay

alsobedesiredtomaintaincontinuedinteractionswithotherswhohavenotadoptedthe

innovationyet.Thisminimizessocialcosts,andmayallowthepreservationof"network

effects,"benefitsofaninnovationwhichscaleaccordingtothenumberofusers(Katz&

Shapiro,1985).Examplesofbackwardcompatibilityininnovationincludetheabilityto

playgamesfromanoldervideogamesystemwithanewerone,ortheabilityofusersof

newertechnologiessuchascellulartelephonesandvoice‐over‐IPtoconnecttousersof

land‐linetelephones.Whenthesecompatibilitiesarenotavailable,adoptionofnew

technologieswillpresumablyproceedmoreslowly.

1.4.2.Conformityasanadaptivebias

Imitationinhumansocialactivitiesbringstomind"conformity,"whichhasnegative

connotationsinbothcommonusageandinmuchofthesocialpsychologyliterature.Some

ofthesenegativeconnotationscanbetracedbacktoAsch's(1951)classicstudiesof

22

conformityinvolvedmeasuringtheeffectofagroupofunanimousconfederatesonthe

visualjudgmentsofnaïveindividualparticipants.However,theearlyemphasisonthe

prevalenceofundesirablebehaviorsintheresultsofexperimentssuchasAsch'shasbeen

moderatedinrecentre‐evaluationsofthedata(Hodges,2004),andcallsforamore

balancedexaminationofthecomplexityoftheenvironmentalmoderatorsandmotivesof

biaseslikeconformity(Krueger&Funder,2004).Forinstance,arecentmeta‐analysisof

125studiesusingtaskssimilartoAsch'sexperimentshowedthattheeffectofthesizeof

theconfederatemajoritygroupdependedonwhetherresponsesweregivenpubliclyand

face‐to‐faceorprivatelyandindirectly,whichisthoughttodeterminethetypeof

conformityprocess(normativeorinformational,respectively)thatdominatesthesituation

(Bond,2005).

Modelinghasshownthatthetendencytoimitateothersratherthaninnovate

(“conformitybias”)canbeadaptiveinuncertainenvironments(Boyd&Richerson,1985;

Kameda&Nakanishi,2002).Similarly,socially‐influenced"informationalherding"

behaviorhasbeenproposedasanexplanationforphenomenasuchasfadsandfinancial

panics(Bikhchandani,Hirshleifer,&Welch,1992;Eguíluz&Zimmerman,2000),butithas

beenarguedthatsuchbehavioristheresultofotherwiseadaptivelyrationalBayesian

reasoninginuncertainconditions(Anderson&Holt,1997;Banerjee,1992;Bikhchandani

etal.,1992).

KamedaandTindale(2006)arguethatconformitybiashasevolvedinhumansand

severalothertaxabecauseofitstendencytopromoteanetaveragebenefitforindividuals

ratherthanerror‐freeperformance.Culturalconventionsarethoughttobeaformoflarge‐

scaleconformitytobehaviorsthatevolvealongwiththeirassociatedpopulations,subject

23

toaccompanyingadaptivepressures(Boyd&Richerson,2005).Oftenthegroup‐levelor

population‐leveloutcomesassociatedwithdecisionsthatareindividuallyrationalarenot

immediatelyapparentorpredictable.Muchlikethesociallearningstrategiesstudiedby

Laland(2004),manycomplexculturalmechanismshaveevolvedtodealwiththisdilemma.

Whentheinteractionofagroupofindividualsinacertainenvironmentisfairlystableover

time,traditionscandevelopwhichdictateexpectationsfor"sensible"behaviorinthat

environment,anddiscourageinnovation.Traditionsmayberelatedtointeractionswiththe

environmentsuchashuntingorfarming,orinteractionswithotherindividualssuchas

marriagecustomsordominancehierarchies.Suchtraditionscanbereinforcedthrough

punishmentofthosewhoviolatethem,rewardsforthosewhofollowthem,orboth.

Traditionscanalsobestabilizedthroughsimpleconformity,thetendencytoimitate

behaviorsthatarecommoninagroup.Whenmembersofagroupimitate,adaptive

solutionstoproblemscanbeeffectivelypreservedwithinaculture.

1.5.Studyinginnovationandimitationinalaboratorysetting

1.5.1.Previouswork

Howcanweprojecttheinfinitespaceofhumaningenuityandsocialcomplexity

ontothecircumscribedstageofacontrolledexperiment?Asidefromflawsinthe

interpretationofAsch's(1951)studiesofconfederateinfluenceonthejudgmentsofnaive

individuals(Krueger&Funder,2004;Friend,Raferty,&Bramel,1990),alargerproblem

withthiskindofexperimentisinitstreatmentofconformityasastaticinfluencerather

thanpartofadynamic,interactiveprocess.Changesincultureandtechnologyinvolvelarge

numbersofagentsinteractingoverlongtimescales,andthegenerationandexchangeof

24

informationbetweenpeoplecannotrealisticallybetreatedasaseriesofisolatedevents.

Whileignoringsociallymediatedinformationinalaboratorysettingmayyieldaclearstudy

ofimportantcognitiveprocessesofindividualproblemsolvingandchoice,inmany

situationsitrepresentsanunrealisticconstraint,andmaylimittherelevanceor

applicabilityoftheconclusions.Asch,andthevastmajorityofthesubsequentresearch

inspiredbyhisstudiesofconformity,madethemethodologicalchoiceofcreatingjudgment

situationswithasinglehumansubjectsurroundedbyaccomplicesoftheexperimenter

whowerescriptedtogivespecificjudgments.Thismethodisjustifiedfromtheperspective

ofcreatingawell‐controlledexperimentalenvironmentforexploringfactorsaffecting

isolatedindividualchoicestoimitate.However,thecostsofthismethodareroughly

twofold.First,constrainingthejudgmentsofallbutoneparticipantinagroupmeansthat

mutualinfluencesininnovationandimitationcannotberevealed.Second,limitingthe

opportunitiesforresponsetoasingletrialforeachjudgmentmeansthatchangesinthese

mutualinfluencesaredifficulttostudy.Theimpactofindividualinnovationandimitation

choicesonthegroup’sperformancecanbestberevealedbyallowingallparticipantsina

decisionmakingtasktobenaturally,spontaneously,andrepeatedlyinfluencedbyone

another.Understandingthegroupdynamicsofimitationandinnovationisoneofthemain

goalsofourstudy,andsoweallowallgroupmembers’theopportunitytoinfluence,andbe

influencedby,eachotherovertime.

Theextensiveliteratureon“groupdynamics”(e.g.Hare,1976;Forsyth,2006)

providesinsightintomanyinterestingprocessesofinteractioningroups,butmuchofitis

focusedoninterpersonalvariablesandspecificsettingssuchasclassroomdiscussion,jury

deliberation,orworkplacecollaboration.Whilethesearecertainlyfascinatingand

25

worthwhiletopics,theyoftenprioritizerealismandapplicationtothesesettingsatthe

expenseofcontrolandgeneralizability,andthusforourpurposestheyremainanindirect

influence.Amoredirectinspirationisderivedfromstudiesofthe“emergence”ofcollective

behaviorfromrelativelysimpleinteractionofindividuals(Holland,1999).Mason,Jones,

andGoldstone’s(2008)studyofgroupexplorationofaone‐dimensionalspaceservesasa

foundationforourstudyinamorecomplexdomain,andwewillwilluseitforcomparison

toourresultslater.

1.5.2.Experimentaldesignandgoals

Conceptually,wecandistinguishbetweentheoptions(behaviors,tools,foods,etc.)

availabletobeexplored,andthelearningstrategies(individualorsociallearningofvarious

types)usedtoexploreandexploitthoseoptions.Wecanalsothinkofchangesinsuch

strategiesovertimeasaformoflearningatahigherlevel.Inthecontextofanexperiment,

wewouldliketobeabletoclearlydesignandmanipulatetheoptionsandstrategies

availabletoparticipants,withoutexcessivelyconstrainingbehavior.

Manylearningtaskscanbeseenascombinatorialpuzzles‐‐choosingacombination

ofmoreorlesswell‐knownpartsorsubtaskstocreateamorecomplexbehavior.Such

combinatorialproblemsareanalogoustoexplorationofalargespaceofpossible

combinations.Ifparticipantshavetheabilitytosampleoptionsfromtheenvironment

throughasociallearningstrategies,oradoptthemfromothersthroughsociallearning

strategies,wecanobserveseveralimportantphenomena:varyingcombinationsof

elementsinparticipants'tentativesolutions,varyingmixturesoflearningstrategiesin

participants'choices,andvaryingproportionsofparticipantstrategiesingroups

26

attemptingtosolveproblemssimultaneously.Thesevariationscanbeobservedwithin

groupsovertime,orbetweengroups(e.g.thosewithdifferentnumbersofmembers,or

havingaccesstodifferentamountsorkindsofinformation).

Withthisinmind,weconstructedtwoexperimentalparadigmswithrecognizable

parallelsinreal‐lifeexploratoryandlearningactivities,inwhichparticipantscansample

andsharecombinationsofelementsfromalarge(butfinite,well‐defined,andstably

related)set,suchthatallchoicescanbeevaluatedaccordingtoanobjectivefunction,while

allowingforalargedegreeofflexibilityandvariationinchoicesandlearningstrategies

overtimeandacrossindividualsandgroups.

Incontrasttoseveralpreviousstudies(e.g.Rogers,1988;Boyd&Richerson,1995;

Kameda&Nakanishi,2002),weusedataskenvironmentthatdoesnotchangeovertime,

andenabledprovisionofregular,reliablescorefeedbackaboutparticipants'ownsolutions,

aswellasthoseoftheirpeers.Thesefeaturescouldbeexpectedtodiscourageexploration

oftheproblemspace,inthatthereisnopenaltyforperpetualexploitationofexisting

solutionsorrepeatedimitationofothers'solutions.Inaddition,theproblemspacewas

designedtobelargerandmorecomplexthaninthosemodels,inordertoprovidegreater

realismintheformofalargernumberofoptionsforexploration,aswellassubstantial

uncertaintyaboutoptimalsolutionsandstrategies.

However,byimplementingtheabovechangesandexplicitlyinstructingparticipants

tofocusonagoalofmaximizationofcumulativeperformance,wehopedtosimplifythe

taskwhilemimickingcharacteristicsofreal‐worldproblem‐solvingenvironments.Inour

task,solutioninformationcannotbecomeoutdatedinthesenseofinaccuracy,butits

performancecanbecomerelativelylesssatisfactorygivencontinuingopportunitiestofind

27

bettersolutions.Thisisanalogoustopracticaltechnologicalprogress,inthatolder

technologiesoftenstillfunctionadequatelyfortheirdesignedpurpose,butnewer

technologiescanprovideimprovementssuchasextrafeaturesormorereliable

performance.Ifthegoalistomaximizecumulativeperformance,someriskmaybe

rationallyjustifiedtoenablegreaterfuturerewards.

Thisapproachisofcoursenotideallysuitedforansweringallquestionsrelatingto

humansociallearning,butitallowsustoapproachavarietyofissueswhichmight

otherwisebetooabstract,varied,andsubtletoreasonablyapproachinacontrolled

laboratoryexperiment,suchastheroleofimitationinconformity,theeffectofindividual

differencesinrisktoleranceorincentiveresponsivenessinthediscoveryofinnovations,

andthecharacteristicsoflearningasacomplex,dynamic,socialendeavor.

1.5.3.Generalpredictions

Basedonthesociallearningstrategiesandtradeoffsdiscussedearlier,wecan

discusssomepreliminarypredictionsaboutparticipants'behaviorandperformance.First,

giventhateveryparticipantwassubjecttothesamechoicepossibilitiesandpayoff

structure,andthepayoffstructurewasfixedforagivengame,weexpectedthatimitation

wouldbemorecommonthaninnovation,becausetheformeroffersimmediaterisk‐free

returns,whilethelatteroffersmoreriskyandvariablereturns.Imitationwouldbebiased

primarilytowardhigher‐scoringsolutions(accordingtopayoff‐biasedstrategies),and

secondarilytowardrelativelysimilarsolutionstotheimitator'sown(duetocompatibility

strategies).Asforoutcomes,anintuitivepredictionbasedontheabovebehavioral

expectationsisthatthehighratesofimitationandsmallamountsofinnovationwouldlead

28

tostagnantgrouplearningprocesses,andalackofsubstantialimprovementsin

performanceovertime.Thispredictionisinlinewithanegativeviewofimitationasstatic,

idleinformationalconformity,butatoddswiththepotentialforgroupstosolvecollective

actionproblemsgivensufficientinformationandincentives(Ostrom,1990).These

predictionswillberevisitedandelaborateduponlaterinthisdissertation.

29

2.Experiment1–PictureGame

2.1.Experiment1overview

Inordertoexplorethedynamicsofinnovationandimitationingroups,andto

attempttoarbitratebetweenthecompetingpredictionsregardingindividualincentives

andgroupconsequences,wedesignedanexperimentinwhichnetworkedgroupsofpeople

exploredahighdimensionalproblemspaceoveraseriesoftime‐limitedrounds.

Participantsreceivedscorefeedbackabouttheirguessesaftereachround,andpassively

sharedinformationabouttheirguessesandscoreswithothers.Participantscouldobserve

andcopythemostrecentguessesoftheirneighborsastheyformedtheirownguesses.

Thedifficultyoftheproblemwasmanipulatedacrossconditionsbychangingthe

sizeoftheproblemspace.Arangeofgroupsizeswastestedtoinvestigatetheeffectsofthe

amountofsocialinformationonindividualperformanceandstrategies.Thein‐game

interactionbetweenplayerswaslimitedtothesimplepassiveexchangeofguess

informationonly,soastoallowexaminationofimitationandinnovationbehavior

unencumberedbymorecomplexsocialinteractions,suchasdirectcommunicationamong

players.

2.1.1.Predictions

Performancewaspredictedtoimproveoverroundswithineachgame,andacross

gameswithinanexperimentsession,duetoscorefeedbackandsimplelearningeffects.

Conversely,solutionturnover(theamountofchangeinasolutionbetweenrounds),and

thediversityofsolutionswithinagroup,wereexpectedtodecreaseovertimeas

30

participantsfoundmorepartsofthecorrectsolution,narrowedtheirsearchtosmaller

areasoftheboard,andrefinedtheirsearchstrategies.

Imitationwasexpectedtobemorecommonofpeerguesseswithhigherscores,

becauseutilitiesofguessesareexplicitandthusimitatorscanmaximizetheirexpected

utilitiesbychoosingthehighestscoringguesses.Imitationwasalsoexpectedtobefocused

onguessesthatweremoresimilartotheimitator'sownpreviousguess,asnotedabove.

Participantswhoimitatedmostoftenwereexpectedtoobtainbetterscoreperformance

(relativetothosewhoimitatedlessoften),becausetheywouldpresumablyimitategood

solutionswhiletakingfewerrisks.Theaveragescoresofparticipantsinlargegroups

(greaterthan4participants)wereexpectedtobegreaterthanthoseinsmallgroups,

becausethelargergroupswouldproduceagreaterdiversityofsolutions,andthusbeable

tosearchtheproblemspacemoreefficiently,contingentontheabilityofparticipantsto

makeuseofthisincreaseddiversitythroughselectiveimitation.

2.2.Experiment1Methods

145participantswererecruitedfromtheIndianaUniversityPsychologicaland

BrainScienceDepartmentundergraduatesubjectpool,andweregivencoursecreditfor

takingpartinthestudy.Participantspopulatedeachsessionbysigningupatwillfor

scheduledexperimentswithamaximumcapacityof9persons,andweredistributedacross

39sessionsasshowninTable2.1.

31

Table2.1:DistributionofParticipantsAcrossGroupSizes

Groupsize 1 2 3 4 5 6 7 8 9

#Sessions 8 6 9 3 3 5 1 2 2

#Participants 8 12 27 12 15 30 7 16 18

Weimplementedtheexperimentusingcustomsoftwareruninawebbrowser,and

eachparticipantusedamousetointeractwiththeexperimentalgame.Allparticipants’

computerscommunicatedwithagameserver,whichrecordeddataandupdatedscores

andteaminformationforparticipantsattheendofeachround.Thetaskwasaround‐

basedpicture‐matchingpuzzlegamewithscorefeedbackgivenaftereachround.Thegoal

picturethatparticipantsattemptedtomatchwasarandomlygeneratedsplinequantizedto

agridofsquarepixels.Thesquaresmakingupthesplinewerecoloredblack,andthe

remainingsquarescoloredwhite(seeFig.1forexamples).

Figure2.1:ExamplesofrandomlygeneratedgoalpicturesinExperiment1.

Theparticipant’sgameboardwasagridofthesamedimensionsasthegoalpicture,

witheachsquareinitiallycoloredwhite.Thecolorofeachsquareonthegameboardcould

betoggledbetweenblackandwhitebyclickingitwiththemouse.Eachparticipant’s

32

displayincludedtheirowngameboardandmostrecentscore(givenasthenumberof

squares,bothblackandwhite,markedcorrectlyoutofthetotalnumberofsquaresonthe

board),theirneighbors’gameboardsandscores,andindicationsofthecurrentroundin

thegameandtheamountoftimeremaininginthecurrentround(seeFig.2).Playerscould

copyaneighbor’smostrecentsolutiontotheirownatanytimeduringthegamebyclicking

thechosenneighbor’sboardwiththemouse.Eachgameconsistedof24roundsof10

secondseach1.Afterthelastroundineachgame,participantswereshowntheirguesses

andscoresforeachround,alongwiththegoalpicture,andabuttontoclickwhenthey

werereadytobeginthenextcondition.Whenallparticipantshadclickedthisbutton,the

nextconditionbegan.

Figure2.2:Exampleofaparticipant’sdisplay.

1 Inapilotstudy,we foundthatusingagamestructurewithhalf thisnumberofroundsandtwice the timeperround

yieldedfairlylowaverageandfinalperformancemeasures,andagreatdealofobservedparticipantidlenesstowardthe

endofeachround,whichpromptedthechangetoprovidingmorefrequentfeedbackinthecurrentgamestructure.

33

Participantswereinstructedtomaximizetheirscoresoverallroundsbymatching

thehiddengoalpictureascloselyaspossible.Theywerealsoinformedthatthepicture

theyweresupposedtomatchineachgamewasrandomlygeneratedandnot

representativeofanyparticularobject,shape,orsymbol,andwasgenerallynot

symmetrical;thattheblacksquareswereallconnectedtoeachothervertically,

horizontally,ordiagonally;andthatthenumberofblacksquareswassmallrelativetothe

sizeofthegrid.Followingtheinstructions,theparticipantsweregiventhefirstcondition,

afterwhichtheexperimenterconfirmedthateachoftheparticipantsunderstoodthe

mechanicsofthegame,andansweredanyquestionsthatarose.Theparticipantsthen

playedtheremainderoftheconditions,withanorderwhichwasrandomizedwithineach

session.Attheendofeachgame,participantswereshownthegoalpicture,alongwiththeir

guessesandscoresineachround.

Aparticipant’sscoreineachroundwasdefinedasacell‐by‐cellcomparison

(overlap)betweentheparticipant’sguessforthatroundandthehiddengoalpicture(i.e.

thenumberofcellswhichthetwopictureshadincommon),dividedbythetotalnumberof

squaresinthegoalpicture,togiveapercentagewhichcouldbecomparedbetween

conditionsofvaryinggridsize(seeFig.3).Animprovementwasdefinedasaninstanceofa

participantobtainingascorehigherthanallpriorscoresofallplayerswithinaparticular

condition.Eachparticipant’snormalizedimprovementsharewasdefinedastheir

individuallyachievedproportionofthetotalimprovementsachievedbyallparticipantsin

asession,multipliedbythenumberofparticipantsinthesession.Avalueof1indicateda

“fair”share,e.g.aparticipantachievedonethirdoftheimprovementsinathree‐person

34

session.Aparticipant’sscorerankinaparticularroundwasdefinedastherankoftheir

score(onebeingthebest)amongallscoresinthegroupinthatround;individualswiththe

samescorehadthesamerank.Turnoverforeachround(afterthefirst)wasameasureof

theamountofchangebetweenaparticipant’sguessesoversuccessiverounds.Itwas

definedconverselytosimilarity,exceptthatthetwopicturescomparedwerethe

participant’sguessesfromthecurrentroundandthepreviousround.

Figure2.3:Score/overlapcalculation:thefirsttwopictureshave20outof25squaresin

common(shownindarkgreyontheright),sotheyhaveanoverlapof80%.

Imitation(ameasureofwhetheraparticipantcopiedaneighbor’sguessina

particularround)wasdefinedasfollows:

€

Ipr =1:maxi(overlap(Gp,r,Gi,r -1)) > overlap(Gp,r,Gp,r -1)0 :maxi(overlap(Gp,r,Gi,r -1)) ≤ overlap(Gp,r,Gp,r -1)

;p ≠ i

WhereGp,ristheguessofParticipantpforRoundr,Gi,r­1istheguessofNeighborifor

theRoundpriortoRoundr,andoverlapisthecomparisondescribedaboveforthescore

calculation.Inotherwords,aparticipanthasimitatedinaparticularround(Ipr=1)ifthe

35

participant’sguessisclosertothemostsimilarneighbor’spreviousguessthantothe

participant’sownpreviousguess.

Diversity(ameasureofthespreadofgroupmembers’guessesovertheproblem

spacewithinaparticularround)wasdefinedasfollows:

€

Dr =1−majority(Gspr)

p∑

s∑

StotPtot

WhereGspristhebinaryvalue(blackorwhite)ofsquaresintheguessofparticipant

pinroundr,Stotisthetotalnumberofsquaresinthegameboard,Ptotisthetotalnumberof

participantsinthegroup,andmajorityisabinaryfunctionthatconveyswhetherthevalue

ofGsprisinagreementwiththemajorityofparticipantsinthegroupforthatsquareinthat

round(0=notinmajority,1=inmajority).Diversityasdefinedaboveisconstrainedtobe

withinthe0to1range,andhighervaluesofdiversityindicatemoredeviationof

individuals’guessesfromthemajorityguesses.

Thenumberofsquaresinthegameboardwasmanipulatedacrosstwoconditions:

inthesmallboardsizecondition,thegameboardwas7squaresoneachsideforatotalof

49squares,andinthelargeboardsizecondition,thegameboardwas9squaresoneach

sideforatotalof81squares.Thelargerboardwashypothesizedtobemoredifficultto

fullysearch.Therewere4repetitionsofeachcondition,foratotalof8gamesineach

session.Theprobabilitydistributionofscoresamongallpossiblegameboardstatesineach

oftheboardsizeconditionsdescribedaboveisshowninFig.4.Thesizeofthegroup

participatingineachsessionwastreatedasacovariate;groupsizerangedbetween1and9.

36

Anotherfactorconsideredwasthe(randomized)positionofeachconditioninan

experimentsession;thiswascalledthegameorder.

(a)Boardsizeof49 (b)Boardsizeof81

Figure2.4:Distributionofscoresforallpossiblegameboardstatesineachboardsize

condition.Notethatduetothenumberofpossiblegameboardstatesineachcondition

(approximately5.6x1014and2.4x1024,respectively)themeanoverallandfinalscores

appeartofalloutsideofthedistributions,butinfactarejustveryrarescoresintheupper

tails.

2.3.Experiment1Results

Formostanalyses,dependentvariableswereaveragedacrossallparticipantswithin

agrouptogivemeasuresforthegroup’saggregateactivity.Inthismanner,the

fundamentallevelofanalysiswasthegroup,nottheindividual,anddependenciesbetween

individualswithinagroupdonotleadtoelevatedTypeIstatisticalerrors.

37

2.3.1.Boardsize/difficulty

Intheaggregate,participantsachievedfinalscoresof.893(i.e.89.3%oftheway

fromtheworstscoretothebestscore),andaveragescores(overallrounds)of.833%.

Meanfinalscoreswereslightlybutsignificantly(about2percentagepoints)lowerinthe

largerboardsizecondition(t(38)=‐2.88,p=.006;seeFig.2.4).Theaverageguessturnover

rateperroundwas7.3%ofthegameboard,andparticipantsengagedinimitationon

25.8%ofguesses.Therewerenosignificantdifferencesinturnoverorimitationrate

betweenthetwoboardsizeconditions.

2.3.2.Rounds

Thedatawereaveragedacrossallparticipantsandallconditionsineachgroupto

givedependentvariablemeasuresforeachgroupwithineachround.Linearmixed‐effects

modelswereusedtoexaminetrendsacrossroundsforeachdependentvariable,witha

randomeffectofgroupmembershipontheslopeoverrounds.Apreliminaryexamination

ofguesscontentconfirmedexperimenterobservationsthatparticipants’firstround

guessesoften(approximately18.5%ofthetime)consistedofallwhitesquares,becausethe

resultingscorewouldrevealhowmanysquareswerecorrectlymarkedaswhite,andthus

howmanyblacksquareswereinthesolution.Thiswasacleverandusefultacticfor

participants,buttendedtoskewtrendsacrossrounds.Forthisreason,thefirstroundwas

excludedfromanalysis.

Analysisofscoreversusroundshowedastronglysignificantpositivetrend

(F(1,857)=139.91,p<.0001,β=0.577;seeFig.2.5a).Similarly,astronglysignificant

negativetrendwasobservedforturnoverversusround(F(1,857)=169.06,p<.0001,β=‐

38

0.527;seeFig.2.5b).Asignificantnegativetrendwasalsofoundforimitationrateversus

round:participantstendedtoimitateeachotherlessoftenaseachgameprogressed

(F(1,713)=14.37,p=.0002,β=‐0.182;seeFig.2.5c).Guessdiversitywassubjectedtoa

similaranalysisafternormalizingitforparticipantgroupsize,whichwasaccomplishedby

dividingallvaluesbythemeandiversityvalueinthesecondroundfortheappropriate

groupsize,whichwasgenerallyatornearthemaximumduetothefirst‐roundblank‐board

phenomenonnotedabove.Theanalysisshowedthatthediversityofguessesinagroup

decreasedsignificantlyoverthecourseofagame(F(1,713)=33.38,p<.0001,β=‐0.415;see

Fig.2.5d).

(a) (b)

39

(c) (d)

Figure2.5:(a)Meanscoreincreased,while(b)turnover,(c)imitationrate,and(d)guess

diversitydecreasedasmoreroundswereplayedwithinagame.

2.3.3.Gameorder

Similarlinearmixed‐effectsmodelswereusedtoexaminetrendsfordependent

variablesacrossgameorderwithinsessions,averagedacrossallparticipantsandall

roundsineachgame.Onceagain,participantgroupwasusedasarandomeffectineach

model.Analysisofscoreversusgameordershowedasignificantpositivetrend

(F(1,272)=52.69,p<.0001,β=0.437;seeFig.2.6a),whileasimilaranalysisofturnover

showedasignificantnegativetrend(F(1,272)=23.08,p<.0001,β=‐0.305;seeFig.2.6b).

Imitationincreasedsignificantlyacrossgameorder(F(1,246)=11.86,p=.0007,β=0.214;see

Fig.2.6c),whileguessdiversitydecreasedsignificantlyacrossgameorder(F(1,111)=7.27,

p=.0081,β=‐0.282;seeFig.2.6d).

40

(a) (b)

(c) (d)

Figure2.6:(a)Meanscoreand(c)imitationrateincreased,while(b)turnoverand(d)

guessdiversitydecreasedasmoregameswereplayedwithinanexperimentalsession.

2.3.4.Groupsize

Amildupwardlineartrendwasobservedforscoreversusparticipantgroupsize

(F(2,36)=4.56,p=.0395),aswellasamarginalquadratictrendwhichpeakedatagroupsize

of4(F(2,36)=4.33,p=.0446;seeFig.2.7a).Similar,strongerupwardlinear(F(2,28)=24.07,

p<.0001)andquadratic(F(2,28)=16.94,p=.0003;seeFig.2.7c)trendswerealsofoundfor

41

imitationrateversusgroupsize.Nosignificanttrendswerefoundforturnoverorguess

diversityacrossgroupsize,althoughbothdisplayedsubstantialvarianceacrossgroup

sizes,andbothseemedtobegenerallyinverselyassociatedwithscore(seeFig.2.7b&

2.7d).

(a) (b)

(c) (d)

Figure2.7:(a)Meanscoreand(c)imitationrateshowedsignificantquadratictrendsacross

participantgroupsizes,while(b)turnover(d)guessdiversityshowednosignificant

trends.

42

2.3.5.Scoredifferenceandrankinimitation

Analysesofthetargetsofimitationshowedthatnearlyallinstancesofimitation

wereofthosewithhigherscoresthantheimitator’s(seeFig.2.8a),implyingthatimitation

behaviorwasgenerallypurposefulandnotrandom.However,therewasastrongbiasfor

imitatingthetop‐scoringsolutioninsmallergroupsthatweakenedsubstantially

(indicatingthatitwasmoredifficult)inlargergroups(seeFig.2.8b).

(a) (b)

Figure2.8:(a)Nearlyallimitationwasofguesseswithhigherscoresthantheimitator’s,

and(b)therewasastrongbiastowardimitatingtop‐scoringparticipants,whichweakened

inlargergroups.

2.3.6.Learningstrategy

Tofurtherinvestigatetherelationshipbetweenstrategyandperformance,we

performedregressionanalysesofscoreversusmeanratesofimitationandturnoverfor

43

individualsandgroups.Notingthepeakingtrendsforscoreandimitationacrossgroupsize

insection2.3.4,andthedifferenceinimitationtargetsacrossgroupsizeinsection2.3.5,we

splitgroupsizesapproximatelyinthemiddleoftherangecoveredintheexperiment,into

thosewith4orfewerparticipants,andthosewith5ormore.Alinearregressionofmean

individualscoreversusmeanindividualimitationrateshowedasignificantpositive

relationshipforthoseingroupsizesof4orless(F(1,49)=7.69,p=.008,β=0.368),butnone

ingroupsof5orlarger(seeFig.2.9a).Likewise,asignificantpositiverelationshipwas

foundbetweenmeangroupscoreandmeangroupimitationrateingroupsof4orsmaller

(F(1,16)=9.92,p=.006,β=0.619)butnoneingroupsof5orlarger(seeFig.2.9b).Acrossall

groupsizes,therewasasignificantpositiverelationshipbetweenanindividual’sscoreand

themeanimitationrateofallothergroupmembers,excludingtheindividual

(F(1,135)=11.68,p<.001,β=.282;seeFig.2.9c);thatis,regardlessofwhatanindividualdid,

she/hewaslikelytohaveahigherscoreiftheothersinher/hisgroupimitatedmoreoften.

Similaranalysesofscoreversusmeanturnovershowedstrongnegativerelationshipsfor

allgroupsizes,atalllevels:forindividualscoreversusindividualturnover

(F(1,143)=198.9,p<.0001,β=‐0.763;seeFig.2.10a),groupmeanscoreversusgroupmean

turnover(F(1,29)=34.59,p<.0001,β=‐0.738;seeFig.2.10b),andindividualscoreversus

groupothers’meanturnover(F(1,135)=40.0,p<.0001,β=‐0.478;seeFig.2.10c).In

addition,forimitativeguesses,weestimatedavaluefor“innovation”bycalculatingthe

proportionofanimitativeguesswhichwasdifferentfromboththeimitator’sprevious

guessandtheguessthatwasimitated.Thecorrelationofscoreswiththisvaluewerenearly

identicaltothosefoundforturnoverabove.

44

(a) (b) (c)

Figure2.9:Forsmallergroups(<5participants),higherscoreswereassociatedwithhigher

imitationratesforboth(a)individualsand(b)groups;however,theserelationshipsdidnot

holdforlargergroups.(c)Forallgroupsizes,regardlessofaparticularindividual’s

imitationrate,theindividual’sscoretendedtoincreaseastheimitationrateofothersinthe

groupincreased.

(a) (b) (c)

Figure2.10Higherscoreswereassociatedwithlowerturnoverratesfor(a)individualsand

(b)groups,aswellasfor(c)individualsrelativetotheturnoverratesofothersinthegroup

(regardlessoftheindividual’sturnoverrate).

2.3.7.Improvements

45

Anexaminationofparticipants’normalizedimprovementshareshoweda

distributionwithanunequalskew;approximately57.7%ofallparticipantsachievedless

thana“fair”improvementshareof1,whileasmallminorityachievedmuchhighershares

(seeFig.2.11).Inordertocomparethedistributionsofimprovementsumswithan

outcomegeneratedfromarandomprocess,weconstructedaPoissondistributionof

improvementsumsforeachparticipantgroupwithlambda(meanvalue)equaltothemean

improvementsumforthatgroup,andfoundtherangeofvalueswhichcontained50%of

thedensityinthisartificialPoissondistribution.Inover80%ofgroupswithmorethanone

participant,the50%densityrangefromtheassociatedPoissondistributioncontainedless

than50%ofthedensityoftheactualindividualimprovementsums,indicatingthatthey

hadagreaterskewthanwouldbeexpectedbychance.

Figure2.11:Histogramshowingtheunequaldistributionofimprovementsacrossthe

participantswithingroups.(Avalueof1indicatesanevenshare,e.g.anindividualachieved

one‐thirdofthetotalimprovementsinathree‐persongroup.)

46

Meanoverallscoreshowedastrongpositivecorrelationwithimprovementshare

(F(1,105)=46.89,p<.0001,B=0.350)Themeanturnoverrateforguessesthatresultedin

improvementswassignificantlysmallerthanthatofnon‐improvements(0.055for

improvementsvs.0.074fornon‐improvements;t(2040)=12.11,p<.0001).Nosignificant

differencewasfoundformeanimitationrate.

2.3.8.Guesssimilarity

Acomparisonbetweenthesimilarityofimitators’mostrecentguessestothose

whichtheyimitated,andtothosewhichtheydidnotimitate,revealedthattherewas

significantlygreatersimilaritytoimitatedguessesthantonon‐imitatedguesses(.777for

imitatedvs..723fornon‐imitated;t(4914)=‐18.23,p<.0001;seeFig.2.12a).Inotherwords,

imitationtendedtobebiasedtowardguessesthatweremoresimilartotheimitator’sown

priorguess.Thisdifferenceheldoverallroundswithinagame(seeFig.2.11b),even

thoughmeanguessdiversitydecreasedoverroundssuchthatsolutionsgenerally

converged(seeFig.2.5d).Nosignificanttrendswereobservedinlinearregressionsof

similarityversusimitatedscorerank,orthescoredifferencebetweenimitatorandimitated

participants.

47

(a) (b)

Figure2.12:Similaritybiasforimitation.(a)Imitators’previousguessesshowedgreater

similaritytotheguessestheyimitatedthantothosetheydidnotimitate.(b)Thebias

towardimitatingmoresimilarguesseswasconsistentacrossallroundsinagame.

2.4.Experiment1Discussion

2.4.1.Dynamicsandstrategies

Thelargerboardsizehadasignificantnegativeeffectonfinalscores,which

confirmeditsuseasaproxyforproblemdifficulty,butthischangeindifficultyhadno

significanteffectontheotherdependentvariables.However,weobservedrevealing

patternsinparticipants’behaviorthatgavesomecluesabouttheirstrategies.

Increasingmeanscoresacrossroundsandgameordershowedthatparticipantsin

groupslearnedthetaskandtheirdrawingsconvergeduponthecomputer’s“secret”picture

overroundsofonegameandoverthecourseoftheentiresession.Participants

accomplishedtheirimprovementsthroughtheuseoffairlyconservativestrategies,as

evidencedbythelowmeanturnoverrate.Furthermore,thedynamicsofthesestrategies

48

causedsolutionstobecomeincreasinglyentrenchedoverthecourseofthegame.This

happenedintwoways(whichmayhavebeenmutuallyreinforcing):participants’ratesof

imitationandgeneralturnoverdecreasedacrossrounds,andtheimitationthatdidoccur

wasbiasedtowardmoresimilarsolutions.Thisentrenchmentcarriedovertothegroup

levelaswell,shownbythedecreasinggroupsolutiondiversityacrossrounds.Ofcourse,

thisresultislikelypartiallyduetoparticipantsconvergingtowardthegoalpicture,butthe

averagefinalscoreofapproximately89%ofthemaximumsuggeststhatgroupmembers’

solutionsoftenconvergedbeforefindingtheoptimalsolution.

Theproblemspaceusedinthistaskisquitelarge(ontheorderof5x1014possible

solutionsforthesmallerboardsize),andanychangetoasolutionbymorethanonepixel

caneasilyresultinasituationwherescore‐decreasingchangescanceloutscore‐increasing

changes,whichmakesscorefeedbackdifficulttointerpret.Inaddition,thenatureofthe

problemispurelylinear–eachcorrectsquareaddsthesameamounttothetotalscore,and

therearenointeractionsthatmakethesearchproblemmorecomplex,orincentivized

largechangesoversmallones.Thusitmakessensethathighscoreswereconsistently

associatedwithlowturnover,andthatmeanturnoverwassignificantlylowerforguesses

thatresultedinimprovements.Ratherthanlarge,revolutionarychanges,participantsmade

small,incrementalimprovementsbychangingonlyafewcells,typicallyjustone.These

smallchangesallowedparticipantstomakeaccurateinferencesabouttheireffectson

score.

Theunequallyskeweddistributionofimprovementswithineachgroupshowedthat

notallparticipantswereskilledatfindinggoodnewsolutions,thoughimitationallowed

someparticipantstotakeadvantageofotherparticipants’innovationsandmaintainhigh

49

meanscores.Thefactthataverageturnoverwashigherfornon‐improvementguesses

shows,however,thatnon‐improverswerenotjustidlywaitingtoimitateothers’

improvements.

2.4.2.Benefitsofimitation

Imitationwasbiasedtowardhigher‐scoringandmore‐similarguesses,asexpected.

Thelatterallowedparticipantsawaytotakeadvantageofothers'goodsolutionswhile

maintaininglowturnoverandhighercontinuitywiththeirownpreviousguesses,

preservingthevalueoftheirexistingknowledgeoftheproblemspace.

Theassociationofhigherscoreswithgreaterimitationratesatboththeindividual

andgrouplevelsinsmallergroups(whowerebetterabletodistinguishthetop‐scoring

guesswhenimitating)showsthatimitationisnotnecessarilyharmfultoinnovationand

performanceimprovements.Inaddition,theassociationofhighindividualscoreswithhigh

imitationratesbyothersinthegroup(regardlessoftheindividual'sbehavior)indicatesa

systemicbenefitforimitationthatdoesnotaccordwithaviewofimitationasapurelyself‐

benefitingact.Itmaybethat,regardlessoftheintentionsofindividuals,imitationbenefits

thegroupbyactingasafilterforpropagatingandpreservingthebettersolutionsavailable

inagroupatagiventime,aswasfoundinarecentcompetitionofsociallearningstrategies

inasimulatedenvironment(Rendelletal.,2010).Thoughitwasreasonabletoexpect

improvementstobeassociatedwithalowerimitationrate(becausethosewhoonlyimitate

otherscannotdobetterthanthosetheyimitate),wefoundthattherateofimitationwas

aboutthesameamongimprovementsandnon‐improvements,whichmeansthatimitators

wereoftenbuildingontheguessestheyimitatedtocreateimprovements.Improvements

50

wereoftenachievedbyimitatingarelativelysuccessfulparticipant’ssolutionandthen

slightlytweakingthissolution.Oncetweaked,theimprovedsolutionwasthenavailableto

otherparticipants,includingtheindividualwhowasoriginallyimitated.

2.4.3.Imitationinformationoverload?

Therewasanunexpectedlylowerbenefitforimitationinlargergroups,asshownby

thelackofassociationbetweenimitationandscoreinlargergroups,whichwaspresentfor

smallergroups.Largergroupscanbethoughttoprovidemoreinformationaboutthe

distributionofsolutionstotheirmembers,becausetherearemoremodelsforeachgroup

membertoobserve.Thiscanalloweachofthemtomakemoreinformeddecisionsabout

whomtoimitateandwhatchangestomaketotheirguesses.However,itmayhavebeen

thatforlargergroupsizes,theamountofinformationprovidedwasmoredifficulttosearch

andcompare,whichledtomorerandomimitationdecisions(asindicatedbytheweaker

biastowardimitatingthetop‐scoringguess)andthuspoorerconvergenceongood

solutions.Itisunlikelythatthiswaspurelyastatisticalartifactofrandomchoiceamong

moreoptions,becausetherewasauniversaltendency(acrossallgroupsizes)toimitate

better‐scoringpeersthanoneself,arelativelyeasierthingtoaccomplishthanfindingthe

bestscore,butdecidedlynon‐random.So,thoughscoreinformationwasreadilyavailable,

itmayhavebeensubjecttocognitiveloadeffects(Sweller,1988).Largergroupswouldbe

expectedtoshowagreatervarianceinsolutionqualitybychance,butanincreasing

inabilitytoproperlydistinguishgoodsolutionswouldcanceloutthisbenefit.

51

2.5.Conclusions

Thoughourassumptionsaboutparticipants'imitationstrategies(favoringhigher‐

scoringandsimilarguesses)wereempiricallysupported,therelatedpredictionsofpoor

performancewerenotborneout.Therewasaconsistentbenefitforindividualstobein

high‐imitationgroupsregardlessoftheirownbehavior,andimitationwasalsoassociated

withbetterindividualandgroupperformancewhenitcouldbedoneselectivelyand

accurately.

Inshort,thetheoreticalimitation‐relatedsocialdilemmadidnotcauseatragic

outcome,whichisconsistentwiththebenefitfor"conformitybias"foundinprevious

modelsandexperimentsofsociallearning(Boyd&Richerson,1985;Kameda&Nakanishi,

2002),andwiththeliteratureonsocialdilemmaswithrepeatedinteractionsand

recognitionofacollectiveactionproblems(Ostrom,1990).Infact,thedegraded

performanceoflargergroupswaslikelyduetoanimpedimenttoimitation.

2.5.1.Modificationsandmotivations

Thefirst‐gamediscontinuityfortrendsinscore,turnover,andimitationindicated

thatthefirstgameineachsessionmighthavefunctionedasapracticegame,duringwhich

participantswerestilllearningthemechanicsoftheexperiment.Thissuggestedthat

explicitpracticeshouldbeincludedinfutureexperimentsbeforedatagatheringbegins,in

ordertoobtainmoreconsistentdata.Inadditiontothefirst‐roundblankboardstrategy

notedabove,participantswereoccasionallyobservedattemptingtocreateimagesonthe

gridcorrespondingtopatterns,symbols,andalphanumericcharacters,despiteinstructions

tothecontrary.Thisisanunderstandableresponsegivennaturalhumancreativity,the

52

presumablylowvisualorconceptualinterestinthegoalpictures,andpotentialsuspicion

aboutexperimenterdeception.Thesebehaviorsaddedsomenoisetothedata.Thelinear

natureoftheproblemandlackofinteractiveeffectsbetweensolutionelementsmayhave

resultedinalackofvariationfromtheslowandincrementalstrategiesweobservedinthis

experiment.

Theseissuessuggestseveralmodificationsforsubsequentexperiments:(a)amore

engagingtask,with(b)lesspossibilityforperformingthetaskinawaythatdepartsfrom

itsintendedpurpose,(c)aclearerandmoreintuitiveinterfaceandinstructions,(d)more

frequentfeedbacktoparticipantsabouttheirperformanceduringthegame(i.e.more

rounds),(e)moreexplicitrecordingofparticipantchoicesforimitation,innovation,etc.,

and(f)asmaller,morediscreteproblemspace(toimprovebothparticipant

comprehensionandtractabilityofanalyses)withinteractiveeffectsbetweensomesolution

elements(toobservepossiblevariationsinexplorationstrategiesfromthoseinthis

experiment).

Inthisstudywefoundthatthebehaviorofisolatedindividualsattemptingtosolvea

complexproblemdiffersmarkedlyfromthatofpeopleconnectedingroups,andthat

differencesinthesizeofagroupcanhavesignificanteffectsonbehavior.Overall,thereare

strongimplicationsinthesedatafortestingthepredictionsofpastworkintheareaof

groupproblem‐solvingbehavior,andpotentialapplicationstomanyreal‐worldproblems.

Theresultspresentseveralintriguingareasforfurtherstudy,whichwedecidedtoexplore

usingataskmodifiedaccordingtotheguidelinesabove.

53

3.Experiment2–CreatureGameA

3.1.Experiment2Overview

InordertoaddresssomeoftheissuesinExperiment1notedabove,wedesigneda

newtaskthatincorporatedthematicelementsofpopulargamessuchasvirtualpetsand

fantasysportsleagues(thoughtheparametersofthetaskwerelimitedtomakeitmuch

simplerthaneitherofthese).Theparadigminvolvesparticipantstryingtomaximizethe

scoreofachosensubsetofindividualunitsfromalargersetoveraseriesofrounds.

Participantscanseetheselectionsofothersineachroundandimitatetheminwholeorin

part,andtheunitsthatparticipantschoosefromareassignedindividualaswellaspairwise

interactionpointvalues.Thesizeandcomplexityoftheproblemspace(andthusthetask

difficulty,asinExperiment1)weremanipulatedviathesizesofthesetofselectableunits

andthesubsetthatcouldbechosenandevaluatedatonetime,aswellasthenumberof

pairwiseinteractions.Weincludedthoroughwrittenandoralinstructionstoparticipants,

aswellasopportunitiesforhands‐onpracticewiththetaskbeforedatacollectionbegan.

Wechangedtheinterfacetomakescorefeedbackclearer(providingemphasisonthesize

anddirectionofscorechangesaftereachround).Wealsounambiguouslydefinedand

determined(ratherthanhavingtoestimate)instancesofimitation,innovation,andso

forth,byrecordingthesourceofeachplayer’sselectionsintheinterface.

3.1.1.Predictions

Thenewtaskalsoallowedustogatheradditionalexplicitdataaboutthe

proportionsofthesourcesofparticipants’solutionelementchoices,includingInnovation

(theintroductionofsolutionelementswithoutpriorassociatedscorefeedback),and

54

Retrieval(thereinstatementofpreviouslyusedsolutionelementsafterchangingthem),

whichwerenotavailableasseparateclassificationsinExperiment1,aswellasImitation

andRetention(roughlytheinverseofturnoverfromExperiment1).

Imitationwasexpectedtobegreateringreaterdifficultyconditions(reflectingthe

greaterriskinalargerandmorecomplexproblemspace),andInnovationwasexpectedto

decrease.Ingeneral,InnovationwasexpectedtoberelativelyrarecomparedtoImitation,

duetoitsrelativelyhigherrisk.RetentionandRetrievalwereexpectedtoincreaseover

rounds(andthusInnovationandImitationwereexpectedtodecrease),asparticipants

narrowedtheirsearchtosmallerareasoftheproblemspace.Weexpecteddecreasesin

InnovationandRetrievalandanincreaseinImitationinlargerparticipantgroupsizes,

becauseparticipantswouldbeabletorelyonalargerpoolofgoodpeersolutionsto

imitate,whichwouldreducetheneedtoexploreorrelyontheirownprevioussolutions.

Thenewtaskwasgenerallyintendedtomaintainthesameoverallcharacterofthe

taskinExperiment1,whilecorrectingafewissues.Thereforeweexpectedthattheresults

wouldshowthesamegeneralpatternsobservedinExperiment1,withtheexceptionof(1)

smoothertrendsofdependentvariablesacrossgameorder(asopposedtothe

discontinuityinthefirstconditioninExperiment1)duetobetterinstructionandhands‐on

demonstrations;and(2)roughlymonotonictrendsacrossgroupsize(asopposedtothe

peakedquadratictrendsinExperiment1),duetointerfaceimprovementsallowing

participantstosearchandcomparepeersolutionandscoreinformationmoreefficiently.

55

3.2.Experiment2Methods

201participantswererecruitedfromtheIndianaUniversityPsychology

Departmentundergraduatesubjectpool,andweregivencoursecreditfortakingpartinthe

study.Participantspopulatedeachsessionbysigningupatwillforscheduledexperiments

withamaximumcapacityof9persons.49sessionswererun,and10sessions(containinga

totalof48participants)werediscardedduetonetworkorsoftwareproblems.The

remaining153participantsweredistributedacross39sessionsasshowninTable3.1.

Table3.1:DistributionofparticipantsacrossgroupsizesinExperiment2

Groupsize 1 2 3 4 5 6 7 8 9

#Sessions 8 6 5 5 5 2 4 3 1

#Participants 8 12 15 20 25 12 28 24 9

Weimplementedtheexperimentusingcustomsoftwareruninawebbrowser,and

eachparticipantusedamousetointeractwiththeexperimentalgame.Allparticipants’

computerscommunicatedwithagameserver,whichrecordeddataandupdatedscores

andteaminformationforparticipantsattheendofeachround.Inthegameitself,

participantsattemptedtomaximizethenumberofpointsearnedbytheirchosensubsets

(“teams”)fromaset(“league”)ofcreatureiconsover24rounds.Thedisplayincludedan

areafortheparticipant’sowncurrentteam,anotherareathatcouldbetoggledtoshowthe

participant’spreviousroundteamortheirbest‐scoringteamsofarinthegame(alongwith

theassociatedscore),aleagueareawhichshowedalloftheicons(potentialteam

members)thatwereavailableforselection,andindicationsofthecurrentroundinthe

gameandtheamountoftimeremaininginthecurrentround.

56

Ifasessionincludedmorethanoneparticipant,eachparticipant’sdisplayalso

showedtheteamandassociatedscoreforallotherparticipantsinthepreviousround.

Iconscouldbecopiedfromanypartofthedisplaytoaparticipant’scurrentteamby

dragginganddroppingthemwiththemouse,exceptforthosealreadyontheparticipant’s

currentteam,whichwerefadedinthedisplayandnon‐clickable.Thecurrentteamcouldbe

replacedentirelybyanotherteambyselectingthescoreboxabovethelatterasa“handle”

anddraggingittothecurrentteamarea.Theorderingofpeers’teamsineachparticipant’s

displaywasnotkeptconstantacrossconditions,toavoidimitationbasedonpastbehavior.

AscreenshotoftheparticipantinterfaceisshowninFig.3.1.

Figure3.1:ExampleofexperimentinterfaceinExperiment2.

57

Atthebeginningofeachsession,playersweregivenahands‐ondemoofthegame

(includingthevariouswaystomovecreaturestoone’scurrentteam),andfurtherinformed

aboutthemechanicsofthegameandwhattoexpectintheremainderoftheexperiment

session,includingthefollowinginformation.Eachgameconsistedof24rounds,andeach

roundwas10secondslong,asinExperiment1.Scorefeedbackwasgivenaftereachround:

iftheparticipant’sscorehadimprovedfromthepreviousround,thenumericalscore

displaycounteduptothenewscoreandturnedgreen,andifithadworsened,thedisplay

counteddowntothenewscoreandturnedred.Attheendofeachgame,thedisplay

showedtheplayer’sfinalscore,alongwithatableofthescoresofeachplayerineach

roundofthegame,whichwassortedbyaveragescore.Theplayer’sownscoreswere

highlightedtoshowtheirrelativeperformancewithoutplacingcompetitiveemphasisonit.

Playerswereinstructedtodotheirbesttomaximizetheirteams’scoresoverall24rounds.

Atthebeginningofeachgame,eachplayer’steamwasarandomselectionofcreatureicons

fromtheleague.

Eachgroupplayed8games,ofwhichhalfhadalargeleagueandteamsize(48and

6,respectively),andhalfweresmaller(24and5).Thesetwoparametersettingswere

intendedtovarythelevelofdifficultyofthegame,withtheformerbeingmoredifficult.

Thiswasbecausealthoughthescoredistributionandcombinatoricsmadehigher

numericalscorespossible,italsomadehigh‐scoringteamsrarerthaninthelattercase:for

thesmallerleaguesize,about4%ofallpossibleteamshadscoresgreaterthan70%ofthe

maximum,whileforthelargerleaguesizethisfigurewas0.4%(seeFig.3.3).Thatis,with

thelargerleagueandteamsize,itwashardertofindgoodsolutionsbecauseofthe

relativelylargenumberofpoorersolutions.

58

Ineachgame,eachiconwasassociatedwithacertainpositivenumberofpoints,and

severalspecialpairsoficonswereassociatedwithseparatescorebonusesorpenaltiesthat

capturedinteractionsbetweenicons.Thescoreforateamwascomputedbysummingthe

individualpointvaluesforeachicon,andthenaddingorsubtractingthevalueofany

specialpairspresent.Thepairsdidnotoverlap,andthedistributionwasdesignedtobe

challenging:pairswhichgavelargepositivebonusesweredistributedamongiconswith

smallindividualpointvalues,andpairswhichgavelargenegativepenaltiesweregenerally

foundamongiconswithlargeindividualpointvalues(seeFig.3.2).

(a)Leaguesizeof24

(b)Leaguesizeof48

Figure3.2:Pointdistributionforindividualicons(boxes)andinteractionbonusesand

penalties(ovals),forleaguesizesof(a)24and(b)48.

59

Individualpointvaluespericonrangedfrom1to8points,andpairinteraction

valuesrangedfrom‐20to20points,sothatthepossiblescorerangesforthelargeand

smallleagueandteamsizecombinationswere[‐6,60]and[‐6,51],respectively.Foreaseof

comparisonandanalysis,allscoreswerenormalizedtotherange[0,1]accordingtothe

rangeofscorespossiblewiththeassociatedleagueandteamsizecombination.The

combinationsofsuchindividualandpairvaluesresultedintheprobabilitydistributionof

scoresamongallpossibleteamsforeachleaguesizeshowninFig.3.3.

Participantswerenotgiveninformationaboutthemaximumscore,thescore

distribution,orthepositionoftheinteractionterms,thoughtheycouldpotentiallyhave

beendeducedduringplay.Theicons’displaypositionandassociationswiththepoint

distributionwereshuffledrandomlyforeachgame,sothattheirappearanceand

placementinthedisplaydidnotgivecluesastotheirpointvaluesduringthecourseofan

experimentsession.

(a)Leaguesizeof24 (b)Leaguesizeof48

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Figure3.3:Distributionofscoresforallpossibleteamsineachdifficulty(leaguesize)

condition.

Ineachround,thefollowingdatawereautomaticallyrecordedforeachplayer:the

iconsonthecurrentteamattheendoftheround(orchoices),thesourceofeachicon,and

theresultingscore.Thesourceinformationindicatedwhethereachiconwasunchanged

fromthepreviousround(Retained),copiedfromtheplayer’sownpreviousroundteam

afterinitiallybeingremovedfromtheteam(Returned),copiedfromtheplayer’sownbest‐

scoringteamsofar(Retrieved),chosenfromtheleaguedisplay(Innovated),orcopiedfrom

anotherplayer’steam(Imitated).WhenImitationwaschosen,thepersistentidentifierof

thecopiedplayerwasrecordedtoallowfurtheranalysesofimitationdecisions.

InthecaseofaplayerreplacingtheentireteamwithImitatedicons,allchoiceswere

recordedasImitated,evenifoneormoreofthemwerealreadyontheplayer’sprevious

roundteam.(ThesamewastrueofreplacinganentireteamwithRetrievedicons,or

removinganiconandthenputtingitbackontheteamviaaLeaguechoice.)However,a

comparisonwiththeplayer’spreviousroundteamallowsthedeterminationofacorrected

choicesourceforeachicon,effectivelyrevealingapotentialincreaseintheRetainchoice

source,andapotentialdecreaseforallotherchoicesourcesexcepttheReturnchoice

source.Inessence,theoriginaluncorrectedchoicesourcesrevealtheliteralactionsof

players,whilethecorrectedchoicesourcesrevealtheireffects.Scoreimprovementsand

scoreranksweredefinedidenticallytothoseinExperiment1.

SimilartoExperiment1,guessdiversityforaparticularroundwasdefinedasthe

proportionoficonsintheleaguerepresentedononeormoreparticipants’teamsduringa

61

givenround.Thisvaluewasnormalizedbytheaverageexpectedvalueofthisproportion

foreachparticipantgroupsize,generatedbyaMonteCarlosimulationassuming

independentrandomteams.(Itshouldbenotedthatthiscalculationandtheassociated

solutionspacesinExperiments1and2areofdifferenttypesandsizesduetothenatureof

thetaskineach.)

3.3.Experiment2Results

Participantsachievedameanoverallscoreof.596(i.e.about60%ofthewayfrom

theworstscoretothebestscore),andameanfinalscoreof.690.Theaverageguesschoice

sourceproportions(originalandcorrected)areshowninTable3.2.TheverylowReturn

ratesuggestedthatanaverageturnoverratedefinedequivalentlytothatinExperiment1

couldbeapproximatedasoneminusthemeanRetentionproportion,or26.1%.(Allfurther

analysesofchoicesourcerefertothecorrectedversions,exceptwherenoted.)

Table3.2:AverageOriginalandCorrectedchoicesourceproportions

ChoiceSource Imitation Innovation Retention Retrieval Return

Original 20.6% 14.0% 59.5% 6.5% 0.5%

Corrected 9.8% 13.7% 73.9% 2.6% n/a

Difference ‐10.2% ‐0.3% +14.4% ‐3.9% n/a

Fortheinitialanalysis,dependentvariableswereaveragedacrossallparticipants

andallroundstogivemeasuresforthegroup’saggregateactivityineachgame.Thesedata

wereanalyzedusingarepeated‐measuresANOVA,treatingeachgroupasasinglesubject,

62

withdifficulty(leaguesize)asawithin‐groupsfactor,thegroupsizeusedasacovariate,

andtheparticipantgroup(sessionidentifier)includedasarandomeffectinthemodelfor

eachdependentvariable.Datafromthefirstroundofeachgamewasexcludedfrom

analysesofchoicesource,becauseseveralchoicesources(Imitated,Retrieved,Retained,

andReturned)areonlydefinedrelativetoapreviousround.Theaboveanalysesrevealed

significantmaineffectsofdifficultyandgroupsizeonscoreandseveralchoicesources,and

asignificantmaineffectofgroupsizeonguessdiversity,aswellasasignificantinteraction

effectbetweendifficultyandgroupsizeonguessdiversity.Theseresults,aswellas

dependentvariabletrendsoverrounds,gameorder,choicesourceuse,scoreperformance,

andguesssimilarityaredescribedindetailbelow.

3.3.1Leaguesize/difficulty

Participantsachievedmeanoverallscores(averagedacrossallrounds)andmean

finalscoresforeachLeagueSizeasshowninTable3.3andFig.3.3.Scoreswerenormalized

asdescribedabove,andpercentilesweredefinedasthepercentageofallpossibleteams

withlowerscoresthantheassociatedmeanscore.

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Table3.3.Meanscore,guessdiversity,andchoicesourceproportionsineachcondition.

LeagueSize

MeanOverallScore

(Percentile)

MeanFinalScore

(Percentile)

MeanGuess

Diversity

MeanImitation

MeanInnovation

MeanRetention

MeanRetrieval

24 .606(90.1%) .693(95.7%) 67.6% 6.8% 16.8% 69.5% 6.3%

48 .539(93.7%) .634(98.5%) 63.4% 7.1% 14.9% 72.1% 5.3%

Diff. ­.067* ­.059* ­4.2%* +0.3% ­1.9%* +2.6%* ‐1.0%

*significantdifferences

Atwo‐samplet‐testwasusedtoexaminethemaineffectofdifficultyoneach

dependentvariable.Itwasfoundthatrelativetothelowerdifficultycondition,thehigher

difficultyconditionresultedinsignificantlylowerInnovation(t(306.8)=2.71,p=0.007),and

significantlygreaterRetention(t(307.5)=‐2.02,p=.0445),butnosignificantdifferences

werefoundforImitationorRetrievalbetweendifficultyconditions,andtrendsforallwere

unchangedforuncorrectedchoicesources.Thehigherdifficultyconditionresultedin

significantlylowerguessdiversity(t(233.8)=2.16,p=.0320),andsignificantlylowerscores

(t(305.8)=7.55,p<.0001;seeFig.3.3).Thescorepercentilesachievedareactuallyhigher

forthelargerLeagueSize,butthisismostlikelyduetothedifferenceintheshapesofthe

twoscoredistributionsused.

3.3.2.Rounds

Linearmixed‐effectsregressionmodelswereusedtoexaminetrendsacrossrounds

foreachdependentvariable,witharandomeffectofgroupontheslope.Analysisofscore

vs.roundshowedastrongpositivetrend(F(1,919)=897.05,p<.0001,β=0.717;seeFig.3.4).

64

Theaverageimprovementinscoreacrossroundswithinagamewas23.7%,andtrendsin

scoresoverroundswerepositiveforallgroupsizes.Guessdiversityshowedasignificant

decreaseacrossrounds(F(1,735)=188.62,p<.0001,β=‐0.404;seeFig.3.4),andsuchtrends

overroundsweremorestronglynegativeforincreasinggroupsize.

Asforchoicesources,Imitationshowedasignificantdecreaseoverrounds

(F(1,681)=126,p<.0001,β=‐0.453),asdidInnovation(F(1,857)=70.78,p<.0001,β=‐0.277).

Theoverallincidencerateofimitationdecreasedsimilarly.Retentionincreased

significantlyacrossrounds(F(1,857)=21.43,p<.0001,β=0.214),asdidRetrieval

(F(1,857)=9.67,p=.0019,β=0.128;seeFig.3.5).Usinguncorrectedchoicesourcesrevealed

nosignificantchangestothesetrends,exceptforslightdifferencesinslope.

Figure3.4:Meanscoreincreasedandmeanguessdiversitydecreasedasmoreroundswere

playedwithinagame;strongereffectswereobservedforlargerparticipantgroupsizes.

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Figure3.5:MeanproportionsofRetentionandRetrievalincreasedandImitationand

Innovationdecreasedasmoreroundswereplayedwithinagame.

3.3.3.Gameorder

Similarlinearmixed‐effectsmodelswereusedtoexaminetrendsacrossgameorder

withinsessionsforeachdependentvariable.Scoredisplayedasignificantupwardtrend

acrossgameorder(F(1,272)=14.69,p=.0002,β=0.186;seeFig.3.6a).Theaverage

improvementinscoreacrossgameorderwithinasessionwas5.6%.Guessdiversity

displayedacorrespondingdownwardtrend(F(1,216)=20.02,p<.0001,β=‐0.180;seeFig.

3.6b).Nosignificanttrendswerefoundfororiginalorcorrectedchoicesourceproportions

overgameorder.

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Figure3.6:Asmoregameswereplayedwithinanexperimentalsession,(a)Meanscore

increased,and(b)thediversityofguessesdecreased.

3.3.4.Groupsize

Trendsacrossparticipantgroupsizeforeachdependentvariablewereexamined

usinglinearmixed‐effectsmodels,withthegroup(sessionidentifier)usedasarandom

effectontheintercept.Scoreshowedasignificantupwardtrendacrossgroupsize,withan

averagescoredifferenceof11%betweenisolatedparticipantsandthoseinthelargest

groupsizeof9(F(1,37)=73.62,p<.0001,β=0.466;seeFig.3.7a).Guessdiversitydecreased

significantlyforlargergroups(F(1,29)=38.25,p<.0001,β=‐0.663;seeFig.3.7b).

Asforchoicesources,Imitationincreasedsignificantlyforlargergroups

(F(1,29)=22.35,p=.0001,β=0.565),andRetentionincreasedaswell(F(1,37)=12.09,

p=.0013,β=0.433),whileInnovationdecreased(F(1,37)=28.95,p<.0001,β=‐0.563),and

Retrievaldecreasedaswell(F(1,37)=12.46,p=.0011,β=‐0.464;seeFig.3.8).Original

(uncorrected)choicesourcesshowednotrendforRetentionacrossgroupsize,but

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otherwisemaintainedthesamepatternofresultsnotedabove,withslightdifferencesin

slope.

Figure3.7:(a)Asparticipantgroupsizeincreased,meanscoresinagroupincreased,and

(b)thediversityofofferedsolutionsdecreased.

Figure3.8:Asparticipantgroupsizeincreased,meanproportionsofRetentionand

Imitationincreased,andInnovationandRetrievaldecreased.

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GiventheresultsforImitationabove,itisimportanttodeterminewhetherthescore

advantageforlargergroupswassimplyanartifactofthegreaterchanceofobservinga

betterscorethanone’sowngiventhelargernumberofguessesbeingmade,leadingto

moreimitationandthushigherscores.Inordertodeterminewhetherthiswasthecase,we

calculatedthescoredifferencevariance(SDV):thevarianceofthedifferencesbetweenthe

top‐rankedparticipantandallotherparticipantswithineachround,averagedwithineach

game.Usingalinearmixed‐effectsmodelliketheothersusedforgroupsizeanalysesabove,

weconfirmedaslightbutsignificantupwardtrendofSDVacrossgroupsize

(F(1,29)=11.37,p=.0021,β=0.262).However,asimilaranalysisofImitationproportionvs.

SDVdidnotrevealanysignificanttrend,andcontrollingforSDVintheImitation

proportionvs.groupsizemodelabovedidnotalteritsignificantly.Inotherwords,the

greaterImitationinlargergroupsdidnotappeartobeduetoincreasedscorevariance.

3.3.5.Scoredifferenceandrankinimitation

Theanalysesinthissectionrefertooriginaluncorrectedchoicesources,because

theirintentistocaptureparticipants’awarenessofotherplayers’scores,notthecontentof

theirguesses.OfallguesseswithgreaterthanzeroImitationproportion,94.3%imitated

onlyoneotherparticipant,5.1%imitatedtwoparticipants,and0.6%imitatedmorethan

twoparticipants.Ofallinstancesofsingle‐participantimitation,82.4%involvedimitation

ofparticipantswhosescorerankwas1(thetopscoreinthegroup),10.7%whosescore

rankwas2,and7%whosescorerankwas3orbelow(seeFig.3.9a).Atthetimeofsuch

single‐sourceimitations,thescoreoftheimitatedparticipantwasgreaterthanthatofthe

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imitatorin89.6%ofcases,equaltoitin2.6%ofcases,andlessthanthatoftheimitatorin

7.8%ofcases(seeFig.3.9b).Nosignificantdifferencesacrossgroupsize,round,etc.were

observedinthesevalues.

(a) (b)

Figure3.9:Therewerebiasestowardimitating(a)better‐scoringparticipantsthanoneself,

and(b)thebest‐scoringparticipant,andthesebiaseswereunaffectedbygroupsize.

3.3.6.Choicesourcestrategy

Thechoicesourcesofeachnon‐isolatedparticipantovertheentiresessionwere

analyzed,andeachparticipant’schoicesourcestrategywascategorizedaccordingtotheir

proportionofeachsource.Participantswhosechoicescontainedonesourceinanaverage

proportiongreaterthantheglobalaverageforthatsourceplusonestandarddeviation,

werelabeledwiththatstrategy.Forexample,aplayerwhoseguessesoverthecourseofa

sessionconsistedofagreaterproportionofImitatechoicesthantheaverageforallother

participantsintheexperiment,plusonestandarddeviation,werelabeledashavingan

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overallstrategyof“Imitate.”Thosewhofittheabovecriteriaformorethanonechoice

source,ornone,werelabeledashavinga“Mixed”strategy.Thescoredistributionfor

playersineachstrategycategoryisshowninFig.3.10(a),withtheRetainstrategyscoring

thebest,followedbyMixed,Imitate,andRetrieve,withInnovatescoringtheworst.

Analysisoforiginaluncorrectedchoicesourcestrategiesshowedasimilarpattern,except

thattheImitateandRetainstrategiesswitchedplaces(seeFig.3.10(b).

(a) (b)

Figure3.10:Scorevs.(a)correctedchoicesourcestrategyand(b)uncorrectedchoice

sourcestrategy,showingthataconservativeandimitativestrategyresultedinthebest

performance.

Theabove‐mentionedfiguressummarizetheresultsofsimpleregressionanalyses

performedforscorevs.individualandgroupuseofeachchoicesource.Alinearregression

ofmeanindividualscorevs.meanindividualImitationguessproportionshoweda

significantpositivetrend–thegreateraparticipant’saverageproportionofImitation,the

bettertheparticipant’sscore(F(1,143)=8.64,p=.0038,β=0.239;seeFig.3.11a).Asimilar

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positivetrendheldforRetention(F(1,143)=55.72,p<.0001,β=0.530;seeFig.3.12a).The

oppositewastrueforindividualscorevs.Innovation,whichdisplayedasignificant

negativetrend(F(1,143)=119.8,p<.0001,β=‐0.675;seeFig.3.13a),asdidRetrieval

(F(1,143)=10.93,p=.0012,β=‐0.267;seeFig.3.14a).Analysesofscorevs.original

uncorrectedchoicesourcesshowedsimilartrendsforImitationandInnovation,butnone

forRetentionorRetrieval.

Averysimilarpatternofresultswasshowninanalysesofmeangroupscorevs.

meangroupguessproportionforeachchoicesource,withupwardtrendsforImitation(i.e.

thehigheragroup’smeanImitation,thehigheritsmeanscore)andRetention,and

downwardtrendsforInnovationandRetrieval(allp<0.001;seeFigs.3.11b‐3.14b).The

onlydifferenceforanalysesofuncorrectedmeangroupchoicesourceswasthelackofa

trendforRetention.Likewise,averysimilarpatternofresultswasfoundforanalysesof

meanindividualscorevs.meangroup(excludingtheindividual)guessproportionforeach

choicesource.TherewasapositivetrendforImitation(i.e.themoreanindividual’sfellow

groupmembersimitated,thehighertheindividual’sscore),aswellasRetention,and

negativetrendsforInnovationandRetrieval(seeFigs.3.11c‐3.14c).Onceagain,theonly

differenceforanalysesofuncorrectedmeangroupchoicesourceswasthelackofatrend

forRetention.Alltrendsnotedaboveweregenerallymonotonic;thatis,therewereno

thresholdsorinflectionpointsbeyondwhichtherelationshipschanged.

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(a) (b) (c)

Figure3.11:Higherscoreswereassociatedwithhigherimitationratesfor(a)individuals

and(b)groups,aswellasfor(c)individualsrelativetotheimitationratesofothersinthe

group(regardlessoftheindividual’simitationrate).

(a) (b) (c)

Figure3.12:Higherscoreswereassociatedwithlowerinnovationratesfor(a)individuals

and(b)groups,aswellasfor(c)individualsrelativetotheinnovationratesofothersinthe

group(regardlessoftheindividual’sinnovationrate).

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(a) (b) (c)

Figure3.13:Higherscoreswereassociatedwithhigherretentionratesfor(a)individuals

and(b)groups,aswellasfor(c)individualsrelativetotheretentionratesofothersinthe

group(regardlessoftheindividual’sretentionrate).

(a) (b) (c)

Figure3.14:Higherscoreswereassociatedwithlowerretrievalratesfor(a)individuals

and(b)groups,aswellasfor(c)individualsrelativetotheretrievalratesofothersinthe

group(regardlessoftheindividual’sretrievalrate).

3.3.7.Improvements

AsinExperiment1,improvementsweretalliedforeachparticipantineachsession.

Ahistogramofnormalizedimprovementshareshowedthatjustoverhalf(54.5%)of

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participantsachievedlessthanthe“fair”shareof1;however,thedistributionispeaked

stronglyaround1,andtherewerenoparticipantswhoobtainedzeroimprovements(see

Fig.3.9).JustasinExperiment1,inordertocomparethedistributionsofimprovement

sumswithanoutcomegeneratedfromarandomprocess,weconstructedaPoisson

distributionofimprovementsumsforeachparticipantgroupwithlambda(meanvalue)

equaltothemeanimprovementsumforthatgroup,andfoundtherangeofvalueswhich

contained50%ofthedensityinthisartificialPoissondistribution.Injustover60%of

groupswithmorethanoneparticipant,the50%densityrangefromtheassociatedPoisson

distributioncontainedlessthan50%ofthedensityoftheactualindividualimprovement

sums,indicatingthattheygenerallyhadonlyaslightlygreaterskewthanwouldbe

expectedbychance.

Figure3.15:Histogramshowingrelativelyequalachievementofimprovementswithin

groups.(Avalueof1indicatesanevenshare,e.g.anindividualachievedone‐thirdofthe

totalimprovementsinathree‐persongroup.)

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The mean choice source proportions for guesses that resulted in score

improvementsandthosethatdidnotareshowninTable3.6.

Table3.6.Meanchoicesourceproportionsforimprovementandnon‐improvement

guesses.

ChoiceSource Imitation Innovation Retention RetrievalProportioninnon‐improvementguesses

9.9% 12.9% 74.9% 1.7%

Proportioninimprovementguesses

8.0% 20.2% 70.0% 1.4%

Difference ­1.9%* +7.3%* ­4.9%* ‐0.3%*significantdifferences

3.3.8.Guesssimilarity

Acomparisonbetweenthemeansimilarityofparticipants’mostrecentguessesto

thosewhomtheyimitated,andtothosewhomtheydidnotimitate,revealedaslightbut

significantdifference:.550forimitatedvs..503fornon‐imitated(t(5029)=‐7.10,p<.0001;

seeFig.3.20).Inotherwords,priortoimitation,theaverageimitators’guesswasmore

similartothatoftheimitatedparticipant(s)thantothoseofothers.Inaddition,the

differencebetweenmeansimilarityforimitatedandnon‐imitatedparticipantsremained

overrounds(seeFig.3.21).Nosignificanttrendswereobservedinlinearregressionsof

guesssimilarityvs.imitatedscorerank,orsimilarityvs.thescoredifferencebetween

imitatorandimitatedparticipants.

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Figure3.16:Similaritybiasforimitation.(a)Imitators’previousguessesshowedgreater

similaritytotheguessestheyimitatedthantothosetheydidnotimitate.(b)Thebias

towardimitatingmoresimilarguesseswasconsistentacrossroundsinagame.

3.3.9Frequencyandmomentumbias

Inordertomeasurethebiasofparticipantstochooseaniconaccordingtoits

frequencyinneighbors’choices,wetalliedthenumberofplayersinthegroupwhoseteams

includedeachiconinthepreviousround(NR‐1),aswellasthenumberoftheremaining

playerswhoaddedittotheirteaminthecurrentroundviaImitationorInnovation.To

convertthesefigurestonormalizedfrequencies,thefirstnumberwasdividedbythe

participantgroupsize(N),andthesecondnumberwasdividedbythenumberof

participantswhodidnotpossesstheiconinthepreviousround(N–NR‐1).Inthiswaywe

wereabletomeasurethemeanprobabilityofImitationandInnovationforanyiconnot

alreadyincludedonaplayer’steam,basedonthefrequencyofitsappearanceon

neighbors’teamsintheplayer’sdisplay.

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Thechanceprobabilityofimitation(resultingfromchoosinganiconatrandomfrom

amongallneighbors’teams)scaleswiththechoicefrequencyofaniconrelativetotheteam

size.Thechancelevelofinnovation(resultingfromchoosinganiconatrandomfromthe

leaguedisplay)isaconstantatoneovertheleaguesize.Sinceleagueandteamsize

conditionswerebalancedinallsessions,weusedtheaveragevalueofeachtocalculatethe

chancebaselines.Alinearmixed‐effectsanalysisofimitationprobabilityversuschoice

frequencyshowedapositivefrequency‐dependentImitationbiasthatwassignificantly

greaterthanchance(F(1,1128)=1648,p<.0001,B=.300;seeFig.3.17a),aswellasasimilar

butmuchsmallerfrequency‐dependentInnovationbias(F(1,1128)=268.7,p<.0001,

B=.062;seeFig.3.17b).Interestingly,theprobabilitiesofImitationandInnovationonly

roseabovechancewhenthemajorityofaparticipant’sneighborspossessedanicon(i.e.

whenChoiceFrequencywasgreaterthan0.5).

(a) (b)

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Figure3.17:Therewerebiasestowardchoosingelementsthatweremorefrequently

representedonotherteamsin(a)Imitationand(b)Innovationdecisions,showingacopy

themajoritystrategy.

Inasimilaranalysisof“choicemomentum,”wetalliedthechangeinthenumberof

playerswhoseteamsincludedtheiconintheprevioustworounds(NR‐1‐NR‐2),aswellas

thenumberoftheremainingplayerswhoaddedittotheirteaminthecurrentroundvia

ImitationorInnovation.Toconvertthesefigurestonormalizedfrequencies,thefirst

numberwasdividedbytheparticipantgroupsize(N),andthesecondnumberwasdivided

bythenumberofparticipantswhodidnotpossesstheiconineitheroftheprevioustwo

rounds(N–max(NR‐1,NR‐2)).Inthiswaywewereabletomeasurethemeanprobabilityof

ImitationandInnovationforanyiconnotalreadyincludedonaplayer’steam,basedonthe

changeinfrequencyofitsappearanceonneighbors’teamsintheplayer’sdisplayoverthe

previoustworounds.

Thedistributionoffrequencychangesforalliconswasverynearlysymmetrical

aroundzero,suchthatanequivalentnumberofpositiveandnegativeproportionchanges

occurred,withsmallabsolutechangesmorecommonthanlargeones.Afterlog‐

transformingtheImitationprobabilitydatatoachieveanormaldistribution,at‐testof

Imitationprobabilityfornegativeandpositivechangesinchoicefrequencyshoweda

significantpositivemomentumbias(t(1236)=18,p<.0001;seeFig.3.18a),andasmallbut

non‐significantmomentumbiasforInnovation(seeFig.3.18b).Therewasalsoasignificant

diminishingofthepositivemomentum‐biasedImitationeffectacrossrounds,butno

changeacrossgameorderorparticipantgroupsize.

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(a) (b)

Figure3.18:Therewerebiasestowardchoosingelementswhoserepresentationonother

teamswasincreasingin(a)Imitationand(b)Innovationdecisions.

3.4.Experiment2Discussion

3.4.1.Dynamicsandstrategies

AsinExperiment1,participants’increasingmeanscoresacrossroundsandgame

orderassuredusthattheylearnedthetaskandwerenotguessingrandomly.Theoverall

characteroftheirstrategiessharedtheconservativepatternofthoseinExperiment1,as

evidencedbythehighmeanproportionofRetention(whichincreasedacrossrounds);this

cautiousapproachwasaccentuatedinthehigherdifficultycondition.Likewise,the

correctedchoicesourceresultsshowedthatmanyguesselementsthatwereinitially

classifiedasImitationorRetrievalwereactuallycomposedoflargelyRetainedelements.

OurpredictionofahighermeanproportionofImitationrelativetoInnovationwas

borneoutinparticipants’intentions(asrecordedintheiruncorrectedchoicesources),but

contradictedintheireffects(correctedchoicesources)–theactualproportionofsolution

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elementsdevotedtoInnovationwashigherthanImitation.Aspredicted,wedidfind

significantlylowerInnovationinthehigherdifficultycondition,butasinExperiment1,

therewasnosignificantdifferenceinImitationbetweenconditions.

Individualguessesbecameincreasinglyentrenchedovertime,asevidencedbythe

decreasingproportionsofinnovationandimitation,andincreasingproportionsof

retentionandretrieval,acrossrounds.Thisbehaviorisconsistentwiththecopywhen

uncertainstrategyinthatmoreimitationoccurredearlyonineachgamewhenparticipants

hadlessexperiencewiththecurrentproblem.Guessesbecameentrenchedatthegroup

levelacrossroundsaswell(asshownbydecreasinggroupsolutiondiversity)despite

decreasingamountsofimitation,becausetheremainingimitationwasincreasinglydriven

byconvergentbiasestowardgreaterguesssimilarity,higherchoicefrequency,andpositive

choicemomentum.Thesebiasesalsohelpexplainthedecreaseinguessdiversityinthe

greaterdifficultyconditionwithoutanaccompanyingincreaseintheincidenceofimitation.

WhereasBaron,Vandello,andBrunsman(1996)foundthatincreasingtaskdifficulty

increasedtheincidenceofimitation,inthisexperimentitappearstohaveinsteadchanged

thefocusoftheimitationthatoccurredtofavorincreasedgroupsolutionhomogeneity.

Thefactthataveragefinalscoresarelessthan70%ofthemaximumpossiblescore

impliesthat,especiallyinlargergroups,participantsaresettlingongoodbutsuboptimal

solutionsduetoinsufficientsearchofthemultimodal,“rugged”problemspace.Thisresult

agreeswiththefindingsofMason,Jones,andGoldstone(2008),thatfully‐connected

groups(liketheonesinthisexperiment)performedrelativelypoorlyonamultimodal

problemspace,whereasmoresparsely‐connectedgroups(latticesandsmall‐world

networks)foundoptimalsolutionsmorereliably,thoughmoreslowly.

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Thelackofsignificantchangesinchoicesourceproportionsacrossgameorder

withinsessionsimpliesthatlearninginthecombinedcontextoftheproblemspaceandthe

groupoccurredanewforeachgame,withoutmajoradaptationsofthemembersofthe

grouptoeachotheroverthecourseofexperiment.Thismayhavebeenduetothelackof

communicationavailablefordiscussingorcoordinatingactionswithinthegroupduring

thesession(Ostrom,Gardner,&Walker,1994).However,guessdiversitydecreasedacross

gameorder,suggesting(aswiththedecreaseacrossdifficultyconditionsnotedabove)

mechanismsofconvergencethatmayhaveoperatedthroughtheabovebiasesinimitation.

3.4.2.Groupsizeeffects(andlackthereof)

ThepredictedincreaseinImitationwithlargergroupsize(afteraccountingfor

artifactualscorevarianceexplanations),alongwithdecreasedInnovationandRetrieval

indicateabiastowardsociallearningthatscaleswiththenumberofmodelsolutionsto

compare,choosefrom,andintegrate,andtheaccompanyingincreaseinscoreindicatesthat

thiswasabeneficialstrategyforthistask.Conversely,thereductioninRetrievalwith

increasinggroupsizeindicatesagreaterdependencebyisolatedindividualsandthosein

smallergroupsonthebuilt‐in“memory”oftheBestScoreoptioninthegameasasourceof

reliablygoodsolutionsonwhichtobuild.Thecombinationoftheseresultsimpliesthatin

largergroups,thisfunctionofmemorymaybe“outsourced”tootherswhoimitateandthus

propagateandpreservegoodsolutionswithinthegroup.Thisphenomenonhasbeen

exploredpreviouslyasa“divisionofcognitivelabor”inthetheoryof“transactivememory”

ingroupcognition(Theiner,2009;Wegner,1986).Adifferentapproachtothecopywhen

uncertainstrategyisshownhere:Imitationisfavoredwhenthepayoffforinnovationis

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relativelyuncertain,comparedtotheabundantinformationavailableaboutthecontent

andutilityofneighbors’guesses.

Weconfirmedtheintuitivepredictions(andthegeneralpatternfromExperiment1)

thatmostimitationeventswereofthetop‐rankedneighbor(confirmingtheuseofthecopy

successfulindividualsstrategy),andofneighborswithhigherscores(confirmingtheuseof

thecopyifbetterstrategy).Theactionsofimitatorswhochosenon‐top‐rankedoreven

lower‐scoringneighborstoimitatewerenotexplainedbysimilaritybetweentheirguesses,

andmayhavebeenduetorandomerrors.Thelackofinfluenceofparticipantgroupsizeon

thisresult(aswellastheroughlymonotonicincreasesinscoreandImitationacrossgroup

size,andthemoreequitabledistributionofimprovementshares)indicatesthatthetask

modificationsweimplementedinthisexperimentseemedtohavetheintendedeffectof

clarifyingthecomparisonofpeersolutionsandscores.

3.4.3.Choicestrategiesandcumulativeinnovation

Therelationshipevidentbetweenperformanceandchoicestrategy,inwhichabove‐

averageRetentionandImitationproducehigherscores,whileabove‐averageInnovation

andRetrievalproducelowerscores,reinforcestheevidencefromExperiment1thatthe

overallconservative(butnotregressive)approachnotedaboveisbeneficialforthistask.

However,acounterpointforthisseeminglysimpleresultisprovidedbythecomparisonof

choicesourceproportionsbetweensolutionswhichgeneratedimprovementsandthose

thatdidnot,whichshowedthatareplacementofsignificantamountsofImitationand

RetentionwithInnovationwasrequiredtocreatenewandimprovedsolutions.Thefact

thatsubstantialamountsofeachoftheabovethreechoicesourceswerepresentinsuch

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improvedsolutionsshowsthatimprovementswerecumulative,relyingonindividuals’own

pastsolutionsaswellasborrowingfromothers.This,inturn,impliesthattheadaptive

valueofImitationinthiscontextisduetoitsfacilitationofselectivelearningandthe

generationofcumulativeimprovementswithlessriskyInnovation(Boyd&Richerson,

1995;Kameda&Nakanishi,2003).

3.4.4.Improvements,free‐riding,andanabsenceoftragedy

Theresultsregardingimprovementsandtheirdistributionwithingroupsindicate

thatparticipantssharedthetaskoffindingbettersolutionsmoreequitablythanifmost

participantswerepursuingapuresocialloafingstrategy.However,thedecreasein

InnovationandincreaseinRetentioninlargergroups,suggestadaptationsbygroup

memberstolimitriskyInnovationtowhatwasrequiredtoachieve“goodenough”results

giventheeffortsofothers.Infact,itmaybethatthelowerendofthedistributionof

Innovationthatactuallyoccurredwasnearlyoptimalfortheverythin‐taileddistributionof

scoresinthespaceofpossiblesolutions(seeFigure23).Only4.3%and1.6%ofpossible

solutionshavehigherscoresthantheparticipants’averagefinalscoreinthelowerand

higherdifficultyconditions,respectively.Thus,althoughtheresultsshowinginequalityin

individualimprovementsharesindicateasubstantialamountoffree‐ridinginthis

experiment,therewasnoassociated“tragedyofthecommons”forInnovations(Hardin,

1968;Ostrom,1990).ThisalsooffersaplausibleexplanationfortheincreasedInnovation

andcorrespondinglowerperformanceofparticipantsinsmallergroups‐‐havingfewer

fellowplayerstocopyfromalsoprovidesfewercluesastothedistributionofpossible

scores,whichpromptsfurtherriskyexplorationatahighercostinaverageperformance.

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3.5.Experiments1and2–GeneralDiscussion

3.5.1.Factorsthatinfluenceimitation–whenandwhomtoimitate

ParticipantsinbothExperiments1and2displayedfairlyconservativestrategies,

typicallypreservingalargeproportionofeachguessfromroundtoround(throughlow

turnoverandhighretention,respectively).Theentrenchmentdynamicsseeninboth

experimentsshowedthischaracteristicintensifyingovertime,asincreasingproportionsof

guesseswerepreservedinlaterrounds.Asforthechangesthatweremade,Laland(2004)

describesseveralstrategiesthatareobservedacrossawiderangeofspecies.Thecopy

whenuncertainstrategyseemedtobethedefaultatthebeginningofbothexperiments,but

forthosewholearnedtherisksofinnovationfirsthand,thecopywhenasociallearningis

costlystrategywasaverylikelynextresort.Participantsalmostuniversallyemployedthe

copywhenbetterandcopythebeststrategiesaswell,andastrategyoffrequency‐

dependentimitationthatcloselyresembledcopythemajoritywasprevalentinExperiment

2.Participantsalsoshowedapositive“momentumbias”towardimitationofsolution

elementsthatwereincreasinginoverallfrequencyinthegroupratherthandecreasing.

Thisphenomenonhasalsobeenshowntooccurinanexaminationofbaby‐naming

decisionsbyparentsasrevealedby130yearsofsocialsecuritydata(Gureckis&Goldstone,

2009).

Characteristicsoftheproblemspaceandtheinformationenvironmentplayeda

substantialroleinthedynamicsofthesestrategiesandtheirconsequences.Theparticipant

groupsize‐dependentpatternsofimitationanditseffectsinExperiment1(andthelack

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thereofinExperiment2)showedtheimportanceofclearandsharablesolution

information.

Itisusefultonotethatthetaskdesigninbothexperimentsallowedparticipantsto

pursuehybridstrategieswithinasingleround,inwhichtheyretainedsomepartsofa

solutionwhilechangingothersusingbothsocialandasociallearning.Oneparticularly

interestingwaythiswasaccomplishedwasthroughsimilarity‐biasedimitation.This

allowedtheimitatortomakeuseofsocialinformationwhilekeepingasolutionpartially

compatiblewithprevioussolutionsandexistingknowledgeoftheproblemspace,a

phenomenondiscussedatlengthinrelationtoinnovationpropagationbyRogers(2003).A

biastowardborrowingfromsimilarratherthandissimilarsolutionshasalsobeen

incorporatedintogeneralmachinelearningalgorithmsfeaturingmultipleagents

simultaneouslysearchingforsolutions(Goldberg,1989).Whenagentsborrowsolution

elementsfromotheragentspursuingsubstantiallydifferentsolutions,thereisastrongrisk

thattheresultingblendofsolutionswillbeasub‐optimalhybridnotwelladaptedtothe

nicheofeitheroftheoriginalsolutions.Byanalogy,twosolutionstopredationforasmall

mammalmightbeevolvelargeclawsforclimbtreeseffectivelyortodeveloplargewings

forflying.However,ahalf‐breedthatcombinesbothsolutionsmightwellenactneither

solutioneffectively.Likewise,giventhecomplexproblemsearchlandscapesusedinthe

experiments,participantsmayhavebeenbiasedtocopysolutionelementsfromsimilar

ratherthandissimilarsolutionstoensuregreatersolutioncompatibility.

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3.5.2Group‐leveleffectsofimitationandinnovation

TheresultsofExperiment1suggestthatimitationcanbeindividually

counterproductivewhensocialinformationcannotbereadilycompared,integrated,and

adaptedtocreatenewsolutions.Thissituationmayariseforseveralreasons:(1)

evaluativeinformationiseitheractuallyunavailable,orpresentedinsuchawaythat

cognitiveloadeffectshinderitsuse;(2)theproblemspaceistoolargeorcomplexforparts

ofdifferentsolutionstobeeasilyanalyzedandcombined;or(3)theproblemspaceistoo

largeforsubstantialchangestobeeffectivelyevaluated.

TheresultsofExperiment2showthatwhentheabove‐mentionedproblemscanbe

avoidedorameliorated,imitationcanbeproductiveforindividualsaswellasgroups,

becauseitenablesthepreservationofgoodtentativesolutionsin“groupmemory”and

theirfurtherimprovementthroughcumulativeinnovation.Theseresultsalsoshowedthat

therisksofinnovationcanoutweighthebenefitsforbothindividualsandgroups,andthus

becomecounterproductivewhenusedtoomuch.Obviously,acompletelackofinnovation

willresultinalackofimprovements(becausestrategiesthatcombineimitatedelements

fromdifferentmodelswilloftenlosebeneficialinteractions),butthisexperimentsuggests

thatinalargeandcomplexproblemspace,atboththeindividualandgrouplevels,

innovationisbestusedsparingly,alongwiththeretentionofpreviousgoodsolutionsand

imitationofothers,toimproveoveralloutcomeswhilemaintaininghighaverage

performance.

Thesetworesultstakentogetherwiththereductionsindiversityovertimeimplya

viewthatisatoddswiththosepredictedfromasimpleTragedyoftheCommons(Hardin,

1968)orproducer‐scroungerdilemma(Kameda&Nakanishi,2002)interpretationof

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sociallearning.Muchlike“conformist,”beinga“scrounger”oftencarriesanegative

connotationordenotation,suchas“socialloafing”(Latané,Williams,&Harkins,1979).

However,suchbehaviormaybeappropriatewhennotallgroupmembers’fulleffortsare

requiredtoproducesufficientbenefit.Inacomplexbutrelativelystableenvironment,the

bestoutcomeforthegroupmayresultfrommostgroupmembersconvergingona“good

enough”solutionquicklytoachievehighmeanperformance,andthenintroducing

productiveinnovationswhenpossible.Thus,insomecircumstancesatragic(oratleast

distinctlysuboptimal)outcomecanresultfromtoomuchinnovationandnotenough

imitation,ratherthantheotherwayaround,becauseinnovationisriskyandpossibly

redundant(andthuswastefulofresources),andimitationhelpstoconcentrateeffortsand

improvethethoroughnessofsearchintheproximityofknowngoodsolutions.Givensome

baselineinclinationtoaminimumamountofindividualexploration,thelimitingfactorin

improvingsearchperformancemaybetheamountofinformationsharingandcoordination

amongsearchers,whichallowthemtopoolboththebenefitsandtherisksofasocial

learning(Hess&Ostrom,2007).

Ofcourse,theresultsobtainedherearelikelytobehighlydependentonthe

problemspaceandtheinformationenvironmentinuse.Thoughthebenefitsofsocial

learninginatemporallystableenvironmentareoftenassumedtobeevident(e.g.Kameda

&Nakanishi,2002),thisstudyilluminatessomedetailsaboutthedynamicindividualand

group‐levelmechanismsbywhichthesebenefitscanaccrue(ornot,insome

circumstances).Givenimperfectindividualmemory,the“culturalknowledgepool”

(Kameda&Nakanishi,2003)requiresnotonlyprovisionofinformationbyasociallearning,

butalsoitsamplificationandpreservationthroughmechanismslikefrequency‐biased

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adoption,or“conformisttransmission”(Boyd&Richerson,1985).Ourtask,inwhich

solutionshavemultiplecomponentswithepistaticrelationships,alsoallowedusto

examinehowsuchsolutionsarebuiltcumulativelyusingselectivelyvaryingproportionsof

differentinformationsources.Thisaddsrealisticcomplexitybeyondthatprovidedby

modelsandexperimentalsettingswithsimplerproblemstructuresorlessflexiblelearning

strategies.

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4.ExplorationasaSocialDilemma

4.1Dilemmasofknowledge

Sofarwehavefoundevidenceforseveralimportantlearningstrategiesdiscussedin

previousmodelsandanimalresearch.Wehavealsoexploredtheideathatcollectivesearch

problemsliketheonesinourexperimentaltasksarepotentiallysusceptibletosocial

dilemmas(thoughwehavenotobservedevidenceforsuchadilemma).However,wehave

notsufficientlyelaborateduponthecharacteristicsofthe"resource"involved,howitis

createdandmaintained,orhowitmightbedegradedordestroyed.Atthispointitwillbe

usefultoreturntotheliteratureonsocialdilemmastopursuethisfurther.

4.1.1.Storiesandassumptions

Socialdilemmascanbesaidtooccur"wheneverindividualsininterdependent

situationsfacechoicesinwhichthemaximizationofshort‐termself‐interestyields

outcomesleavingallparticipantsworseoffthanfeasiblealternatives"(Ostrom,1998).

Contemporaryexamplesoflarge‐scalesocialdilemmasincludethefailuretolimitthe

productionofatmosphericpollutants,andtheoverharvestingofoceanfishstocks.Butsuch

dilemmascanariseinmanyeverydaysituations,fromtrafficjamsatrushhourtofibbingat

taxtime.Socialdilemmashaveoftenbeenframedintermsofthreemetaphoricalstories:

thePrisoner'sDilemma(Poundstone,1992),theTragedyoftheCommons(Hardin,1968),

andtheLogicofCollectiveAction(Olson,1965).

ThePrisoner'sDilemmaisbasedonahypotheticalsituationinwhichtwo

individualsaccusedofcommittingacrimetogetherarequestionedseparatelyandoffered

twochoices:confesstothecrimeorkeepsilent.Ifbothkeepsilent,theauthoritiescanonly

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convictthemonminorchargesandthepenaltyforbothismild.Ifbothconfess,theyare

convictedforthecrimeandreceivesubstantialjailsentences.Ifonlyoneconfesses,hegoes

freewhiletheotherreceivesaharshsentence.Thissetofpossibilitiesissuchthat

whatevertheotherdoes,therational(ordominant)optionforeachindividualistoconfess.

However,ifbothindividualsfollowthisreasoning,thebestoptionforboth(keepingsilent)

isunavailable.(Itmaybethatwedonotwantcriminalstobeabletoescapesucha

dilemma,butthissituationcanbere‐framedinanynumberofotherways,e.g.anarmsrace

betweencountries,steroiduseamongcompetitiveatheletes,etc.)Theactionsofthetwo

agentsareinterdependentsuchthateithercanindependentlyincreasehisownpayoffat

theexpenseoftheother,butthebestoutcomecanonlybeobtainedifbothhavesomeway

totrusttheotherandjointlyincreasetheirpayoffs.

TheTragedyoftheCommons(Hardin,1968)isanotherhypotheticalsituation,in

whichapasture(orcommons)isavailableforusebymanyindividualstograzetheir

animals.Eachadditionalanimaladdedtothecommonsincreasesitsowner'spayoffinthe

shortterm,butreducestheamountoffodderavailableforalloftheotheranimals.Inthe

longterm,overgrazingcanleadtotheruinationofthepasture,sothatnofodderis

available.Themarginalbenefitofaddinganotheranimalisobtainedbyoneindividual,but

theshort‐termcostisspreadacrossallindividualsusingthecommons(anegative

externality).Thismeansthattheshort‐termbenefitsoutweighthecostsforeach

individual;ifallindividualsfollowthisreasoningsymmetrically,thelong‐termbenefits

(continuedgrazingcapacity)areunavailable.Again,thismodelisnotonlyimportantfor

cattlefarmersinagrarianvillages,asitcanbere‐framedtofitmanyothersituationsmore

relevanttomodernsociety(e.g.usinglawnsprinklerssuppliedbyacommonreservoir

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duringadrought).Onceagain,theimportantpointisthattheactionsofmultipleagentsare

interdependentsuchthateachcanincreasehisorherownshort‐termpayoffatthe

expenseofothers,butthebestlong‐termoutcomecanonlybeobtainedifallfindsomeway

tocooperate.

TheLogicofCollectiveAction(Olson,1965)portraystheconflictinherentbetween

theself‐interestsofalargenumberoffirmssellingthesamegood.Themarketforthisgood

ispresumedtobeperfectlycompetitive,butina"disequilibrium"state,sothatprice

exceedsmarginalcostforallfirms.Eachwouldliketomaximizeprofitsbysellingasmuch

ofthegoodastheycanproduceatthehighestpricepossible.However,(undercertain

assumptionssuchashighbarrierstomarketentry,inelasticdemand,andsoforth),firms

thatincreaseproductionwillsellmorebutalsoincreasetheoverallsupply,whichwill

eventuallylowerprices.Anyfirmthatattemptstounilaterallyrestrictitsownoutputin

ordertolowersupplywillsimplyreduceitsrevenues,giventhatnofirmhasenough

marketpowerindividuallytoaffectprices.Allofthefirmshaveacommoninterestin

higherprices,buteachwouldrationallypreferthattheothersbearthecostoflowered

productioninordertogetit.(Onceagain,ifonehastroublefeelingempathyforthefirms

depictedhere,theframingcanbechangedtothatofworkerswhocannotallearna

sufficientwageifeachoffershisfullcapacitytoexploitativeemployers.)InOlson’s

formulation,theonlywaytokeeppriceshighisthroughsomeexternalintervention,such

asgovernmentpricesupports,tariffs,orcartelagreements,thecreationofwhichrequires

costlylobbyingororganization.Assumingthatthefirmssomehowforeseetheproblemand

bandtogethertocollectivelycreatetheprice‐supportingintervention(aslightdeparture

fromtheprevioustwomodels),aproblemremains.Becausethemarketforthegoodis

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indivisible,eachfirmonceagainhastherationalincentivetoenjoythebenefitsofsuch

interventionwithoutcontributingtocreateormaintainit,ifsuchcontributions(lobbying

firmfeesorunionmembershipdues)arevoluntary.Thusthefirst‐orderdilemma

(agreeingtoorganizetocontrolprices)isatleasttemporarilysolved,butthesecond‐order

dilemma(maintainingthecostlyorganization)isvulnerabletoa“free‐riding”problem.

Eachoftheabovethreemodelsillustratesanimportantpointaboutsocial

dilemmas,andthenontrivialityoftheirsolutions.Thoughtheycaneachbeadaptedto

resemblefamiliarsituations,problemsarisewhenthesemodelsaretakentoberealistic

representationsofhumanbehavior.Withoutdenyingthatsocialdilemmascanhavetragic

outcomes,itmustbenotedthatthestoriesabove(andthetheoriestheyrepresent)involve

severaloverlysimplisticassumptionsaboutsocialdilemmas:(1)resourceusersarestrictly

selfishmaximizersofshort‐termgains,whowillnotcooperatetoovercomeasocial

dilemma,(2)itisarelativelysimpleanalyticaltasktochangetheincentivesofresource

usersbydesigningnewrules,and(3)centralizeddirectionandcoercionisrequiredto

successfullyovercomesocialdilemmas(Ostrom,1999).Ingeneral,thethreeassumptions

abovehavenotbeenborneoutbydatagatheredonhumanresponsestosocialdilemmas,

inthelaboratoryorinthefield.Peoplecaninfactrecognizethedilemmastheyface,and

changerulesandincentivestoavoidthem(Ostrom,1990).However,doingsocanbequite

acomplexanduncertainprocess,involvingmuchtrialanderror,andmaynotalwaysbe

successful(Sandberg,2001).Finally,centralizedsolutionshavegenerallynotbeenas

successfulasthosedesignedusingtheknowledgeandparticipationoflocalresourceusers

(Sneath,1998).

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4.1.2.Typesofgoods

Socialdilemmasdealwithpotentialconflictsbetweenagentsoveravaluable

resourceorgood.Twopertinentdimensionsoverwhichgoodscanvaryaresubtractability

(whethertheuseofsomeportionofthegoodbyoneindividualprecludesitsuseby

others),andexcludability(theextenttowhichpotentialuserscanbepreventedfromusing

theresource).Subtractabilityisgenerallyabinarycharacteristic,andsubtractablegoods

arealsoknownasrivalrousgoods,becausepotentialusersarenecessarilyrivalswhenany

portionofagoodcanonlybeusedbyoneofthem,butisdesiredbyall.Whena

subtractablegoodisscarceandnomeasuresareinplacetoprioritizeitsuseamong

individuals(suchaspropertyrightsorotherrules),theexpectedresultisincreased

scarcityandconflict.However,thecharacteristicofsubtractabilitycanbeusedtomonitor

theuseofagood,whichcanhelpinencouragingorenforcingcooperationinadilemma.

Excludabilityisamorecontinuouscharacteristic,andneednotbeabsoluteinordertobe

effective.Physicalandtechnologicalmeansplayarole,butlegal,social,andculturalnorms

areimportantaswell;conceptsoffairness,justice,andtraditioncanallaffectthe

excludabilityofagood.

"Privategoods"arethosewhicharebothsubtractableandexcludable,suchasatool

oraloafofbread."Clubgoods"arethosewhichareexcludablebutnotsubtractable,suchas

accesstocopyrightedworks,orascenicviewfromfencedland.Privateandclubgoodsare

generallypresumednottoentailseriousdilemmas,becausetheirownersorproviderscan

excludepotentialusers,anduserscanavoidthosewhichareinefficientlyprovided.

Goodswhicharesubtractablebutforwhichexclusionisimperfectorcostlyare

knownas"commongoods"or"commonpoolresources"(CPRs).Instancesoftheseinclude

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fisheries,forests,andthecanonicalexampleofpasturelands.Common‐poolresourcesare

typicallyself‐renewingatsomefiniterate,butadilemmamayobtainifindividual

incentivesdonotsustainappropriationoftheresourceandavoidoveruseordestruction.

TheyhavetypicallybeenthoughtofaccordingtotheTragedyoftheCommonsmodelas

describedabove.

Goodsthatareimperfectlyexcludableandnon‐subtractableareknownas"public

goods."Instancesoftheseincludegenerallyintangibleorindivisibleitemssuchas

televisionbroadcastsandthelightfromlighthouses,respectively.Theprimarypotential

dilemmaforpublicgoodsisthe"free‐riding"problem:howsuchgoodscanbesufficiently

providedandmaintained,sincetheycanbeusedbyindividualswhodon'tcontributeto

theirprovision(freeriders).Aconnectedproblemishowtoassurethosewhowishto

contribute(butdon'twanttowastetheircontribution)thatotherswilldosoaswell,

insteadoffree‐riding(theassuranceproblem).Thisdilemmaisoftenmodeledusingthe

LogicofCollectiveActionparadigmdescribedabove.

PublicGoodsandCommonPoolResourcesareconceptuallyandnaturallyrelated,in

thataCPRoftenrequiresaninitialorcontinuinginvestmentintheprovisionofinstitutions

andinfrastructurerelatedtoappropriation.Thisinvestmentallowscurrentandfuture

userstoparticipateintheappropriationoftheresource;thatis,theinputsthatcreatethe

benefitoftheinstitution'scontinuedexistencearerivalrouseveniftheresourceitselfis

not.Themoregeneralclassesofprovisionandappropriationproblemsaretypically

modeledandtreatedseparatelyinordertoelucidateusefulcharacteristicsinalleviating

eachtypeofproblem(Ostrom,Gardner,&Walker,1994).

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4.1.3.Knowledgeasacommons

Thetaskofunderstandingknowledgeasagoodaccordingtotheabovetaxonomy

canbeabittricky,becauseknowledgecantakevariousformsthataresubjecttodifferent

usesandnorms.HessandOstrom's(2007)treatmentof"KnowledgeasaCommons"begins

bydefining"knowledge"as"alltypesofunderstandinggainedthroughexperienceor

study"(p.8).Inthisintangibleform,knowledgeappearstobeapurepublicgood.Firstly,it

isquitedifficulttoexcludepotentialusers:asdiscussedinpreviouschapters,humanshave

aprodigioustalentandinclinationforgainingknowledgefromeachother,andoncea

particularideahasbeenunderstood,itisdifficulttoun‐understand(or"derstand"(Currie,

2010))itbyanyreliablemeans,voluntaryorcoercive.Secondly,oneperson's

understandingofanideadoesnotprecludeorsubtractfromanyotherperson's;if

anything,thesharingofunderstandingcanreinforceandpreserveit.

Ofcourse,peoplehavefoundwaystoencodeandrecordthisintangible

understandinginvariousphysicalforms(e.g.paintedtombwalls,incisedclaytablets,

handwrittenpaperscrolls,printedbooks,pressedphonographrecords,celluloidfilm,and

documentsanddatabasesinanynumberofdigitalmedia)inordertoarchiveitandpassit

ontonewpotentialunderstanders.Thevaryingdegreestowhichthesetoolsfor

instantiationofknowledgearesubjecttophysicalandlegalconstraintiswhatcomplicates

thegovernanceofknowledgeasaresource.

Asphysicalobjects,printedmatterandaudiovisualrecordingscanbeprivately

ownedbyanindividualandmadeinaccessibletoothers,orheldbyapubliclibrary

collectionforfullandfreeusebyonepersonatatime,orkeptinamuseum'sdisplaycase

wheretheyareobservablebutnotfullyusable.Images,text,andsoundcanbeencoded

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digitallyandcopiedmoreorlesseffortlessly(thoughtheymustalwaysbestoredinsome

physicalform).

Despitethenon‐rivalrousnatureofintangibleknowledge(andastransmissionand

storagebecomecheaper,perhapsanydigitizableknowledge)asapublicgood,some

resourcesrequiredtocreateit(money,tools,etc.)arecertainlyrivalrous.Totheextentthat

knowledgedependsonmorethanonepersonforitsprovision,theclassicalassurance

problemofcollectiveactionobtains.Totheextentthatthecreationofnewknowledge

dependsontheuseofpreviouslyexistingknowledgeand(1)thephysicalinfrastructureof

knowledgestorageandaccessrequiresresourcesformaintenance,or(2)knowledgecan

beappropriatedandaccessprevented,dilemmasofunderprovisionandoverappropriation

becomepossible.

Finally,ifa"commons"isdefinedsimplyasa"asharedresourcethatisvulnerable

tosocialdilemmas"(Hess&Ostrom,2007,p.13),itiseasytosee"knowledgeasa

commons."ForHessandOstrom(2007),analysisofanycommonsrequiresexaminations

ofequity("issuesofjustorequalappropriationfrom,andcontributionto,themaintenance

ofaresource"),efficiency("optimalproduction,management,anduseoftheresource"),

andsustainability("outcomesoverthelongterm").Wewillreturntothesethreecriteriato

judgeresultsofourexperimentsandthoseofotherstudies.

4.2.Influenceofinformationenvironmentonsociallearningstrategies

Sofarwehavenotfoundevidencefora"tragic"outcomeinunderprovisionof

individualexplorationinourparticipants'collectivesearchbehaviorovertime,extreme

inequityinprovision,orunsustainabilityinlonger‐termresults.Thoughparticipantswere

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ratherconservativeintheirstrategies,innovationwasmorecommononaveragethan

imitation,implyingarelativelackofharmful"freeriding."Improvementsharewasfairly

equitablydistributedwithingroups,andfinalscoreswerequitehighintermsof

percentilesinthedistributionofpossibleoutcomes.However,participantsgenerallydid

notreachoptimalsolutions,sotherecouldbepossibilitiesforimprovingefficiencyand

absoluteperformancethroughchangesinparticipants'incentivesandinformation

environment.Theremayalsobeimportantfactorswhichcouldharmparticipants'abilityto

contributetotheproductionandsharingofinnovations.

4.2.1.Inefficiencyandinformation

Previousworkhasshownthatmakingsociallearningprocesseslessefficientcan

actuallyimprovethelong‐termperformanceofgroupsattemptingtosearchacomplex

problemspace,bothinlaboratoryexperiments(Mason,Jones,&Goldstone,2008)and

agent‐basedmodels(Lazer&Friedman,1997).Thereductioninefficiencywas

implementedinthesestudiesbychangingthedistributionoflinksinthesocialnetwork

connectingparticipants.Thishadtheeffectofslowingthespreadofinformationviasocial

learning,encouraginggreaterexploration,andmaintaininggreatersolutiondiversity

amonggroupmembers,thusavoidingprematuresettlingofthegroup'ssearchongoodbut

suboptimalregionsoftheproblemspace.Havingobservedsomegeneraldynamicsand

learningstrategiesofcollectivesearchintheexperimentsdescribedsofar,wewishedto

seewhetherthisseeminglyparadoxicaleffectwouldoccurwithconceptuallysimilar

changestoourexperimentalparadigm.

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Ourpreviousexperimentshavealsoshownthatthesociallearningstrategiesthat

participantspursuedependontheinformationavailabletoeachparticipant,specificallyin

termsofthenumberofotherparticipantssharinginformationabouttheirtentative

solutions.Presumably,thisisbecauselargernumbersofpeerssharinginformation

increasetheoverallreliabilityoftheinformationavailabletoeach.Aspreviouslydiscussed,

thiscanbeinterpretedasaninstanceofthecopywhenuncertainsociallearningstrategy

(Laland,2004),becausegreatercertaintyaboutthevalidityofsocialinformationincreases

therelativeuncertaintyofasociallearning.Otherworkondiffusionofinnovationshas

shownthattheuseandinfluenceofsocialinformationdependontherelativeambiguityof

thebenefitofadoptingaparticularsolution(Granovetter,1978;DiMaggio&Powell,1983;

Abrahamson&Rosenkopf,1997;Gibbons,2004).Inamodelofsocialforagingbehaviorina

changingenvironment,KrebsandInman(1992)showedthatifthereisadelayinan

observer’srecognitionoftheforagingsuccessofademonstrator,thereisacorresponding

reductionintheinformation(andthusthebenefit)providedbythesocialinformation

providedbythedemonstrator;withalongenoughdelay,theobserverisbetteroffignoring

thedemonstratorandforagingasocially.Anotherresultfrommodelingisthatifpersonal

(asocial)andsocialinformationcannotbegatheredsimultaneously,theremaybeno

benefittousingsocialinformation,becausetheycannotbeeffectivelycombined;

furthermore,whenothers’actionsareavailabletobeobserved,butnottheresulting

success‐relatedcues,socialinformationshouldbeminimizedtoavoidinformation

cascades(Giraldeau,Valone,&Templeton,2002;Bikhchandani,Hirshleifer,&Welsh,

1992).

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4.2.2.MotivationandconceptualdescriptionofchangesinExperiment3

Havingshowninpreviousexperimentsthatparticipantscanuseavarietyof

learningstrategiestosolveacollectivesearchproblem,wewantedtoseehowthese

strategieswouldshiftinresponsetochangesintheinformationenvironment.Ratherthan

changingthestructureofthesocialnetworkconnectingourparticipants(asinthework

citedjustabove),wedecidedtosimplyremoveaccesstoscoreinformationaboutothers'

solutions.Participantswouldstillbeabletoobserveandcopytheirpeers,butwouldhave

towaitfortheirownfeedbacktolearnthevalueofimitatedchoices;informationabout

others'solutionswasentirelyambiguous,whileinformationabouttheirownsolutionswas

entirelyunambiguous.Thisissimilartocontextsinwhichindividualanimalscanobserve

thebehaviorofothers,butnotthecuesoroutcomesthatmotivatethoseactions,or

situationsinwhichprivatefirmscanwithholdinformationaboutrevenues(i.e.thesuccess

oftheiractions)fromcompetitors.

Wewishedtousethisrelativelysmallmodificationtoaskquestionsabouthowthe

eliminationofinformationsupportingonekindofsociallearningwouldcauseparticipants

tochangetheirlearningstrategies,andhowsuchchangeswouldaffectperformance.Asthe

workaboveonimprovedcollectivesearchperformancethroughreducedcommunication

efficiencyindicates,impedingsociallearningmayincreaseasociallearningamongmost

participants.Suchanoutcomewouldpresumablyreducefree‐riding(improvingequityof

provision);butwouldthischangecauseparticipantstoactuallyfindbettersolutions,or

wouldthereducedefficiencyofaccesstopreviousknowledge(andtheinabilitytouseit

simultaneouslywithasocialinformation)reducetheefficiencyofknowledgeproduction?

Presumingthatsociallearningisnotdisplacedentirelybyasociallearning,howwouldits

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prevalenceandusechange,andwhatinformationwouldbeusedtodirectremaining

imitationchoices?Finally,wouldtheseadaptationsinbehaviorimproveoverallindividual

andcollectiveoutcomesandimprovementsovertime(sustainability)?

Inordertoavoidceilingeffectsonperformanceandpresumablymakeiteasierto

distinguishtheperformanceofsuccessfulsocialandasociallearning,wechangedthe

problemspaceslightlyfromthepreviousexperimenttoshiftsomeofthemassofthescore

distributiontoalongerandfatteruppertail(increasingtheproportionofsolutionswith

higherscores).Thisallowedtheparalleldiscoveryofhigher‐scoringsolutionsamong

participantswithoutrequiringasmuchconvergenceofsolutioncontent;performance

couldbeincreasedwithoutnecessarilyconstrainingsolutiondiversity.

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5.Experiment3–CreatureGameB(scorevisibility)

5.1.Experiment3Overview

Thetaskusedinthisexperimentwasthesameasthe“CreatureGame”of

Experiment2,withtwomajorchanges:(1)thescoresassociatedwithpeers’solutionswere

showninhalfthegamesineachexperimentsession,andhiddenintheotherhalf;(2)the

problemspacewaschangedbyaddingmorepositive‐scoringbonusinteractionsbetween

solutionelements,whichhadtheeffectofmakingtheuppertailofthescoredistribution

longerandfatter,sothattherewererelativelymoresolutionswithhighscores.

Modification(1)allowedfortheexaminationofdifferencesinstrategiesandperformance

associatedwithdifferencesintheavailablesocialinformation.Modification(2),thoughit

madedirectcomparisonswithExperiment2slightlymoretenuous,allowedparticipantsto

achievehighscoreswithoutnecessarilyconvergingintheirsolutions.

5.1.1.Predictions

Becauseofthesmallchangeswemadetothetask,weexpectedthatresultswould

bequitesimilartothoseofExperiment2whenpeers’scoreswereshown.Whenevaluative

informationaboutpeersolutionswasunavailable,participantswouldbeunabletobe

sufficientlyselectiveinimitation,andthusparticipantsemployinghighlyimitative

strategieswouldhaverelativelylowerscoresthanthosewithlessimitation‐heavy

strategies,participantswouldemploylessimitationandmoreinnovation,andsolution

diversitywouldincrease.Similarity‐biasedandfrequency‐biasedimitationstrategies

wouldbestrongerwhenpeerscoreswereinvisible,inordertocompensateforthelackof

directevaluativeinformation.Overall,ratherthanimprovingexplorationbehavior,the

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impedanceofsociallearningbymakingpeerscoresinvisiblewouldresultinlowermean

scores(includingthoseofrelativelysuccessfulasociallearners)becausetheywouldbe

unabletoeasilytakeadvantageofgoodsolutionsfoundbyothersthroughselective

imitationandfurtherimproveuponthem.

5.2.Experiment3Methods

234participantswererecruitedfromtheIndianaUniversityPsychology

Departmentundergraduatesubjectpool,andweregivencoursecreditfortakingpartinthe

study.Participantspopulatedeachsessionbysigningupatwillforscheduledexperiments

withamaximumcapacityof9persons,andweredistributedacross65sessionsasshown

inTable5.1.

Table5.1:DistributionofparticipantsacrossgroupsizesinExperiment3

Groupsize 1 2 3 4 5 6 7 8 9

#Sessions 16 8 11 11 7 2 4 4 2

#Participants 16 16 33 44 35 12 28 32 18

ThetaskusedwasnearlyidenticaltothatofExperiment2,withthefollowing

changes.Tomoreeasilyfitthesessionintheone‐hourtimelimitrequiredforexperiments

usingoursubjectpool,thereweresixgamespersessioninsteadofeight.Inthreeofthese

games(theinvisible­scorescondition),thescoresofotherparticipantswerenotshown

alongwiththeirsolutionsfromthepreviousround;intheotherthreegames(thevisible­

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scorescondition),otherparticipants’scoreswereshown.Ofcourse,thisdistinctiononly

matteredinsessionsthatincludedmorethanoneparticipant.

Thedistributionofindividualpointvaluesfortheiconswasthesameasforthe

largerleaguesizeinExperiment2,butsevennewpositivebonusinteractionswereadded

betweenicons,andseveralexistinginteractionvalueswereshiftedtodifferentpairsof

icons,asshowninFig.5.1(comparetoFig.3.2b).Thesechangeshadtheeffectofincreasing

thecomplexityoftheproblemspace,aswellasincreasingthenumberofpossiblehigh‐

scoringteams.Asaresult,thepossiblescorerangechangedto[‐6,88],butallscoreswere

againnormalizedtotherange[0,1]foreaseofanalysis.(Notethatduetothisshift,

normalizedscorescannotbedirectlycomparedbetweenExperiments2and3.)The

combinationsoftheseindividualandpairvaluesresultedintheprobabilitydistributionof

scoresamongallpossibleteamsshowninFig.5.2(comparetoFig.3.3b).

Figure5.1:Pointdistributionforindividualicons(boxes)andinteractionbonusesand

penalties(ovals).

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Figure5.2:Distributionofscoresforallpossibleteams.

5.3.Experiment3Results

5.3.1Overallmeans

MeandependentvariablesineachconditionareshowninTable5.2(seealsoFig.

5.2).Ofallgroupedparticipants,81.7%hadhighermeanscoresinthevisible‐scores

conditionthanintheinvisible‐scorescondition(seeFigure5.3).Isolatedparticipants

achievedmeanoverallandfinalscoresof.356and.395.

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Table5.2.Meanscore,guessdiversity,andchoicesourceproportionsbycondition

Cond.OverallScore(Percentile)

FinalScore(Percentile)

GuessDiversity

Imitation Innovation Retention Retrieval

Visible .447*(92.6%) .523*(97.5%) 62.2%* 9.1% 13.4%* 75.0%* 2.4%*

Invis. .394*(89.1%) .475*(94.6%) 79.0%* 8.4% 15.0%* 71.0%* 4.2%*

IsolatedPartic. .356(81.4%) .395(89.1%) ‐‐ ‐‐ 29.2% 55.8% 13.7%

*significantdifferencesbetweenconditions

Figure5.3:Scattergramofindividuals’meanscoresineachcondition,labeledwiththeir

participantgroupsize.

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5.3.2.Rounds

Linearmixed‐effectsmodelswereusedtoexaminetrendsacrossroundsforscore

andguessdiversity,witharandomeffectofparticipantgroup.Analysisofscoreversus

roundshowedastrongpositivetrendforgroupedparticipantsinthevisible‐scores

condition(F(1,1126)=521.82,p<.0001,B=.656,meantotalincrease=0.220),andaslightly

shallowerpositivetrendintheinvisible‐scorescondition(F(1,1126)=446.53,p<.0001,

B=.727,meanincrease=0.172;seeFig.5.4).Guessdiversityshowedasimilarlystrong

decreaseacrossroundsinthevisible‐scorescondition(F(1,1126)=304.78,p<.0001,B=‐

.443,meanchange=‐0.468),andaweakerdecreaseintheinvisible‐scorescondition

(F(1,1126)=97.31,p<.0001,B=‐0.453,meanchange=‐0.271;seeFig.5.4).Isolated

participants’scoresincreasedmuchless(thoughsignificantly)acrossrounds

(F(1,751)=30.26,p<.0001,B=.348,meanincrease=0.075;seeFig.5.4).

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Figure5.4:Scoresincreasedandguessdiversitydecreasedmoreacrossroundsinthe

scores‐visibleconditionthaninthescores‐invisiblecondition.

Trendsforchoicesourcesacrossroundsshowedverysimilarpatternstothosein

Experiment2:ImitationandInnovationdecreasedsignificantly,andRetrievaland

Retentionincreasedsignificantly.Therewerenosubstantialdifferencesinslopesbetween

conditions,norsubstantialdifferenceswiththeslopesoverroundsfoundinExperiment2.

5.3.3.Gameorder

Similarlinearmixed‐effectsmodelswereusedtoexaminetrendsacrossgameorder

foreachdependentvariablewithinconditions.Forthisanalysis,thegameordervaluefor

eachgamewascorrectedtoitsorderwithinthecondition,i.e.Game1,2,or3ineach

condition.Scoredisplayedaslightbutsignificantincreaseacrossgameorderinthevisible‐

scorescondition(F(1,97)=16.57,p=.0001,B=0.264,meanchange=+0.048;seeFig.5.5),and

asmallbutnon‐significantincreaseintheinvisible‐scorescondition.Guessdiversity

displayedacorrespondingdecreaseacrossgameorderinthevisible‐scorescondition

(F(1,97)=62.09,p<.0001,B=‐0.263,meanchange=‐0.103),aswellasintheinvisible‐scores

condition(F(1,97)=70.79,p<.0001,B=‐0.363,meanchange=‐0.115;seeFig.5.5).

Asforchoicesources,changesovergameorderwithinconditionsweregenerally

slight.Imitationdecreasedslightlybutsignificantlyovergameorderinthevisible‐scores

condition(F(1,97)=6.24,p=.0141,B=‐0.121,meanchange=‐0.011),whileincreasing

significantlyintheinvisible‐scorescondition(F(1,97)=32.97,p<.0001,B=0.289,mean

change=+0.040;seeFig.5.6a).Innovationdecreasedsignificantlyacrossgameorderwithin

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boththevisible‐scores(F(1,97)=26.82,p<.0001,B=‐0.173,meanchange=‐0.028)andthe

invisible‐scores(F(1,97)=41.04,p<.0001,B=‐0.226,meanchange=‐0.036;seeFig.5.6a)

conditions.Retentionincreasedsignificantlyonlyinthevisible‐scorescondition

(F(1,97)=29.97,p<.0001,B=0.252,meanchange=+0.041;seeFig.5.6b),andRetrieval

increasedsignificantlyonlyintheinvisible‐scorescondition(F(1,97)=14.42,p=.0004,

B=0.228,meanchange=+0.012;seeFig.5.6b).

Figure5.5:Scoreincreasedsignificantlyonlyinthevisible‐scorescondition,andguess

diversitydecreasedinbothconditions.

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(a) (b)

Figure5.6:(a)ImitationandInnovationdecreasedsignificantlyinthescores‐visible

condition,whileImitationincreasedandInnovationdecreasedinthescores‐invisible

condition.(b)Retentionincreasedsignificantlyonlyinthevisible‐scorescondition,and

Retrievalincreasedsignificantlyonlyintheinvisible‐scorescondition

5.3.4.Groupsize

Trendsacrossparticipantgroupsizeforeachdependentvariablewithinconditions

wereexaminedusinglinearmixed‐effectsmodels,withtheparticipantgroupusedasa

randomeffectontheintercept.Scoreincreasedsignificantlywithgroupsizeinthevisible‐

scorescondition(F(1,63)=79.59,p<.0001,B=0.580),aswellasintheinvisible‐scores

condition(F(1,63)=15.45,p=.0002,B=0.309;seeFig.5.7),thoughthelattertrendwasnot

asstrong.Guessdiversityshowedacorrespondingdecreasewithincreasinggroupsizein

thevisible‐scorescondition(F(1,47)=68.83,p<.0001,B=‐0.699),aswellasaweakertrend

intheinvisible‐scorescondition(F(1,47)=17.28,p=.0001,B=‐0.430;seeFig.5.7).

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Asforchoicesources,Imitationincreasedsignificantlyforlargergroupsinboththe

scores‐visible(F(1,47)=41.47,p<.0001,B=0.597)andscores‐invisible(F(1,47)=28.04,

p<.0001,B=0.500;seeFig.5.8a)conditions,andInnovationdecreasedsignificantlyfor

largergroupsinboththescores‐visible(F(1,47)=18.42,p=.0001,B=‐0.492)andscores‐

invisible(F(1,47)=14.04,p=.0005,B=‐0.436;seeFig.5.8a)conditions.Retentionincreased

forlargergroupsonlyinthescores‐visiblecondition(F(1,47)=5.91,p=.019,B=0.286;see

Fig.5.8b),whileRetrievalshowednosignificanttrendacrossgroupsize(seeFig.5.8b).

Figure5.7:Asparticipantgroupsizeincreased,meanscoresinagroupincreased,andthe

diversityofofferedsolutionsdecreased,withslightlyweakereffectsforbothinthe

invisible‐scorescondition.

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(a) (b)

Figure5.8:Asparticipantgroupsizeincreased,(a)meanproportionsofImitationincreased

andInnovationdecreasedinbothconditions,and(b)Retentionincreasedonlyinthe

visible‐scorescondition,andRetrievalshowednosignificantchangeacrossgroupsize.

5.3.5.Differencesinimitation

Ofallinstancesofsingle‐participantimitation,thescoreoftheimitatedparticipant

wasgreaterthanthatoftheimitatorsignficantlymoreofteninthevisible‐scorescondition

thanintheinvisible‐scorescondition(t(74)=16.07,p<.0001;seeFig.5.9a);inthelatter

condition,theprobabilitywasabout54%,orapproximatelyatchance.Inaddition,there

wasasignificantlygreaterprobabilityofimitatingthetop‐scoringsolutioninthegroupin

thevisible‐scorescondition(t(80)=20.08,p<.0001;seeFig.5.9b).

Toexamineseparatelyhowoftenandhowmuchparticipantsimitatedoneanother,

wemeasuredthemeanproportionofguessesinwhichtherewasgreaterthanzero

Imitation(Imitationincidence),aswellasthemeanImitationproportioninsuchcases

(Imitationproportion).MeanImitationincidencewassignificantlyhigherinthevisible‐

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scorescondition(F(1,229)=31.17,p<.0001),butthedistributionofmeanimitation

proportionswasweightedsignificantlymoreheavilytowardhighervaluesintheinvisible‐

scorescondition,asshownbyaKolmogorov‐Smirnofftestofequalityofdistributions

(D=0.1893,p<.0001;seeFig.5.10).Inotherwords,participantsinthescores‐invisible

conditioncopiedoneanotherlessfrequentlybutinlargeramountsatatime.

(a) (b)

Figure5.9:Inthevisible‐scoresconditiontherewerestrongbiasestowardimitating(a)

better‐scoringparticipantsthanoneself,and(b)thebest‐scoringparticipant,while

imitationbehaviorintheinvisible‐scoresconditionappearedessentiallyrandomwith

respecttoscoredifferenceandscorerank.

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Figure5.10:ForguessesthatincludedatleastsomeImitation,participantsintheinvisible‐

scoresconditionhadhigherproportionsofImitationintheirguesses.

5.3.6.Choicesourcestrategy

AsinExperiment2,thechoicesourcesofeachnon‐isolatedparticipantoverthe

entiresessionwereanalyzed,andeachparticipant’schoicesourcestrategywascategorized

accordingtotheirproportionofeachsource.Participantswhosechoicescontainedone

sourceinanaverageproportiongreaterthantheglobalaverageforthatsourceplusone

standarddeviation,werelabeledwiththatstrategy.Forexample,aplayerwhoseguesses

overthecourseofaconditionconsistedofagreaterproportionofImitatechoicesthanthe

averageforallotherparticipantsinthatcondition,plusonestandarddeviation,were

labeledashavinganoverallstrategyof“Imitate.”Thosewhofittheabovecriteriaformore

thanonechoicesource,ornone,werelabeledashavinga“Mixed”strategy.Thescore

distributionforeachstrategycategoryineachconditionisshowninFig.5.11.

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(a) (b)

Figure5.11:Scorevs.choicesourcestrategyin(a)visible‐scoresand(b)invisible‐scores

conditions,showingthataconservativehigh‐Retentionstrategyresultedinthebest

performance,thoughasimilarlyconservativehigh‐Retrievalstrategy(returningoftentoa

personalbest‐so‐far)showedgoodrelativeperformanceintheinvisible‐scorescondition.

Theabove‐mentionedfiguressummarizetheresultsofsimpleregressionanalyses

performedforscorevs.individualandgroupuseofeachchoicesource.Alinearregression

ofmeanindividualscorevs.meanindividualImitationguessproportionshoweda

significantpositiverelationship(thatis,thegreateraparticipant’saverageproportionof

Imitation,thebettertheparticipant’sscore),butonlyinthevisible‐scorescondition

(F(1,216)=8.12,p=.005,B=0.190;seeFig.5.12a);nosignificantrelationshipwasfoundin

theinvisible‐scorescondition.Theoppositewastrueforindividualscorevs.Innovation,

whichdisplayedasignificantnegativerelationshipinboththevisible‐scores

(F(1,216)=146.2,p<.0001,B=‐0.635;seeFig.5.12b)andinvisible‐scores(F(1,216)=67.88,

p<.0001,B=‐0.489)conditions.ApositiverelationshipheldforRetentioninboththe

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visible‐scores(F(1,216)=64.6,p<.0001,B=0.480;seeFig.5.12c)andinvisible‐scores

(F(1,216)=13.81,p=.0003,B=0.245)conditions.Finally,apositiverelationshipwasfound

forRetrievalinonlytheinvisible‐scorescondition(SI:F(1,216)=12.73,p=.0005,B=0.236;

seeFig.5.12d).

AsinExperiment2,analysesofmeangroupscorevs.meangroupguessproportion

foreachchoicesourceshowedsimilarrelationshipsofthesamesignificanceanddirections

asthosenotedabove,aswellasanalysesofmeanindividualscorevs.meangroup

(excludingtheindividual)guessproportion,withtheexceptionoftheabsenceofa

relationshipwithRetrievalatbothlevels.Alltrendsnotedaboveweregenerally

monotonic;thatis,therewerenothresholdsorinflectionpointsbeyondwhichthe

relationshipschanged.

(a) (b)

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(c) (d)

Figure5.12:Higherindividualscoreswereassociatedwith(a)higherindividualImitation

onlyinthevisible‐scorescondition,(b)lowerInnovationinbothconditions,(c)higher

Retentioninbothconditions,while(d)higherindividualRetrievalonlyintheinvisible‐

scorescondition.Bestfittinglinearregressionlinesareonlyshownwhenthelinear

relationwassignificant.

5.3.7.Improvements

AsinExperiment1,improvementsweretalliedforeachparticipantineachsession

andcondition.Histogramsofnormalizedimprovementshareshowedarelativelyequitable

distributionofimprovementswithingroupsinthevisible‐scorescondition,witha

distributionstronglypeakedneara“fairshare”of1(56%ofparticipantswerebetween0.4

and1.2),andonly6.4%ofparticipantshavingzeroimprovements;incontrast,therewasa

stronglyinequitably‐skeweddistributionintheinvisible‐scorescondition,withonly36.2%

ofparticipantshavingimprovementsharesbetween0.4and1.2,and21.1%withzero

improvements(seeFig.5.13).AKolmogorov‐Smirnofftestofequalityofdistributions

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indicatedthatthesedistributionsweresignificantlydifferent(D=0.1789,p=0.002).Mean

overallscoreshowedastrongpositivecorrelationwithimprovementshareintheinvisible‐

scorescondition(F(1,168)=64.49,p<.0001,B=0.369),butthisrelationshipwasnotevident

inthevisible‐scorescondition.

Themeanchoicesourceproportionsforguessesthatresultedinscore

improvementsandthosethatdidnotareshowninTable5.3.Inbothconditions,the

proportionofInnovationchoiceswashigherforguessesthatyieldedimprovements

relativetonon‐improvements(invisible‐scores:t(733.20)=‐14.03,p<.0001;visible‐scores:

t(907.73)=‐17.14,p<.0001).Intheinvisible‐scorescondition,theproportionofImitation

choiceswassignificantlylowerforimprovementsthannon‐improvements

(t(916.77)=11.54,p<.0001),whileinthevisible‐scorescondition,theproportionof

Retentionchoiceswassignificantlylowerforimprovementsthannon‐improvements

(t(916.33)=9.34,p<.0001).Ofallimprovementsinthevisible‐scorescondition,24.2%

resultedfromguessesthatincludedImitation,versus12.2%intheinvisible‐scores

condition.In52.3%ofallimprovementsinthevisible‐scorescondition,thefocalplayer

imitatedatleastonepeerwhohadpreviouslyimitatedthefocalplayer,versus41.5%inthe

invisible‐scorescondition.Inotherwords,aplayerwhowasimitatedbyanotherplayer

oftenlaterimitatedthatsameplayerinthecourseofcreatinganimprovement,butthis

happenedsubstantiallymoreoftenwhenscoreswerevisible.

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Figure5.13:Histogramsshowingrelativelyequitableachievementofimprovementswithin

groupsinthevisible‐scorescondition,andaninequitabledistributionintheinvisible‐

scorescondition.

Table5.3:Meanchoicesourceproportionsforimprovementandnon‐improvement

guessesineachcondition.

Condition Improvement %ofguesses Imitation Innovation Retention RetrievalNo 94.6% 9.1% 11.4%* 76.3%* 2.2%Visible

Scores Yes 5.4% 8.2% 19.4%* 69.5%* 2.1%No 95.6% 10%* 13.3%* 71.2% 4.4%Invisible

Scores Yes 4.4% 3.9%* 21.6%* 70.5% 3.5%*significantdifferenceswithincondition

5.3.8.Guesssimilarity

Acomparisonbetweenthemeansimilarityofparticipants’mostrecentguessesto

thosewhomtheyimitated,andtothosewhomtheydidnotimitate,revealedslightbut

significantdifferencesinbothconditions,butinoppositedirections.Inthescores‐visible

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condition,thereweresimilarityvaluesof.563forimitatedvs..524fornon‐imitated

guesses(t(5084)=‐5.47,p<.0001;seeFig.5.14a).Inthescores‐invisiblecondition,there

weresimilarityvaluesof.316forimitatedvs..346fornon‐imitatedguesses(t(4267)=4.35,

p<.0001;seeFig.5.14b).Inotherwords,priortoimitation,theaverageimitators’guess

wasmoresimilartothatoftheimitatedparticipant(s)thantothoseofothersinthescores‐

visiblecondition,andlesssimilarinthescores‐invisiblecondition.

(a) (b)

Figure5.14:(a)Inthescores‐visiblecondition,imitators’previousguessesshowedgreater

similaritytotheguessestheyimitatedthantothosetheydidnotimitate,while(b)inthe

scores‐invisiblecondition,theoppositeeffectwasobserved.

5.3.9.Frequencyandmomentumbias

AsinExperiment1,wemeasuredthebiasofparticipantstochooseanicon

accordingtoitsfrequencyinpeers’choices.Toreiteratebriefly,wemeasuredthemean

probabilityofImitationandInnovationforanyiconnotalreadyincludedonaplayer’s

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team,basedonthefrequencyofitsappearanceonpeers’teamsintheplayer’sdisplay,and

comparedthemtoexpectedchancebaselines.

Linearmixed‐effectsanalysisofimitationprobabilityversuschoicefrequency

showedapositivefrequency‐dependentImitationbiasthatwassignificantlygreaterthan

chanceinthevisible‐scorescondition(F(1,604)=943.25,p<.0001,B=.741),butsignificantly

lowerthanchanceintheinvisible‐scorescondition(F(1,604)=231.67,p<.0001,B=.470;see

Fig.5.15a).Therewasaslightpositivefrequency‐dependentInnovationbiasabovechance

inthevisible‐scorescondition(F(1,604)=181.20,p<.0001,B=.441),andbelowchancein

theinvisible‐scorescondition(F(1,604)=12.78,p=.0004,B=.131;seeFig.5.15b).

Wealsorepeatedtheanalysisof“choicemomentum,”bytallyingthechangeinthe

numberofplayerswhoseteamsincludedtheiconintheprevioustworounds,aswellas

thenumberoftheremainingplayerswhoaddedittotheirteaminthecurrentroundvia

ImitationorInnovation,andnormalizingforgroupsize.Afterlog‐transformingthe

Imitationprobabilitydatatoachieveanormaldistribution,at‐testofImitationprobability

fornegativeandpositivechangesinchoicefrequencyshowedasignificantpositive

momentumbiasinthevisible‐scorescondition(t(640)=‐14.192,p<.0001),andasmaller

positivebiasintheinvisible‐scorescondition(t(661)=‐9.98,p<.0001;seeFig.5.16a).A

slightpositivemomentumbiaswasfoundforInnovationinthevisible‐scorescondition,

butnocorrespondingsignificantbiaswasfoundintheinvisible‐scorescondition(seeFig.

5.16b).

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(a) (b)

Figure5.15:Therewerebiasestowardchoosingelementsthatweremorefrequently

representedonotherteamsinthevisible‐scorescondition,andlessfrequentlyrepresented

onotherteamsintheinvisible‐scoresconditionfor(a)Imitationand(b)Innovation

decisions.

(a) (b)

Figure5.16:Therewerebiasestowardchoosingelementswhoserepresentationonother

teamswasincreasingin(a)bothconditionsforImitationand(b)onlythevisible‐scores

conditionforInnovationdecisions.

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5.4.Experiment3Discussion

Aspredicted,resultsinthescores‐visibleconditionwerequitesimilartothosein

Experiment2,whiletheresultsinthescores‐invisibleconditiondifferedinsomewayswe

didnotpredict.

5.4.1.Differencesinperformance

HavingdemonstratedbenefitsforImitationinthepreviousexperiments,the

impedimenttosociallearningintroducedintheinvisible‐scoresconditionlowered

performanceaspredicted.Thus,thereductionintheefficiencyofsociallearning

implementedbyhidingpeers’scoresdidleadtoincreasedInnovationandsolution

diversity,butdidnotseemtoimprovecollectivesearchperformanceasinMason,Jones,

andGoldstone(2008)andLazer&Friedman(1997).Thisdifferencefromthestudiescited

abovewaslikelyduetothewaythatcommunicationefficiencywasreduced:whereasthey

decreasedtheconnectivityofthesocialnetworkthroughwhichinformationwas

exchanged,weleftthenetworkunchangedbuteliminatedanimportantpartofthe

informationthatparticipantsusedtoguideimitationdecisions.Ourresultsare

substantiallyinaccordancewiththefindingsofGiraldeau,Valone,andTempleton(2002),

whofoundthataninabilitytocombinetheuseofsocialandasociallearning

simultaneouslywouldresultinalackofbenefitforsociallearning;however,wedid

observesomebenefitforsociallearning,inthatparticipantsintheinvisible‐scores

conditionstillperformedbetterthanisolatedparticipants.

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5.4.2.Differencesinstrategy

Overall,thechangeintheavailabilityofperformanceinformationseemedtoshift

participants’tacticsfrommakingsmallchangestotheirguesses,combiningasocialand

sociallearning(incrementaliststrategies)inthevisible‐scorescondition,tomakinglarger

jumpsaroundtheproblemspaceandoftenjumpingbacktopreviousknowngoodsolutions

(saltationiststrategies)intheinvisible‐scorescondition.Thisdifferencewasdiscerniblein

anumberofresults.First,whenscoreswereinvisible,proportionsofInnovationand

RetrievalwerehigherandRetentionwaslower,implyingthatonaverageparticipantswere

keepingsmallerportionsoftheirguessesfromroundtoroundandchangingoftenbetween

newandoldsolutionelements.ThoughtheoverallmeanproportionofImitationwasthe

sameinbothconditions,Imitationwasusedlessoftenandforalargerproportionofthe

guessintheinvisible‐scorescondition–participantsweresignificantlymorelikelytocopy

mostorallofapeer’ssolution.ThelowermeanRetentionintheinvisible‐scorescondition

impliesthatparticipantswereoftenjumpingtoapeer’sguessandeitherkeepingitifit

increasedtheirscore,orjumpingbacktotheirRetrievedpreviousbestguessifitdidnot.

Theabilitytomakeincrementalchanges,mixingelementsfromallsources,should

allowparticipantstoassesstheeffectofsmallerchangesandmakebetterjudgmentsabout

thequalityofindividualelementsandpairsfromotherparticipants;thustherewere

substantialincreasesinscoreacrossroundsandassociationsofRetentionandImitation

withhighscoresobservedinthevisible‐scorescondition.Arelianceonlargeriskyjumps

aroundtheproblemspacewouldlikelypayoffabouthalfthetimeforthemedian

participant,andthosewhojumpedbacktogoodprevioussolutionswouldloselessoverall

thanthosewhocontinuallyjumparound;thustherewereshallowerincreasesinscoreover

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rounds,andanassociationofhigherscoreswithRetrievalbutnotImitationintheinvisible‐

scorescondition.Thissaltationiststrategyseemstohavebeenmoresuccessfulthannot

usingImitationatall,however,asshownbythesubstantiallylowerperformanceof

isolatedparticipants.

Theremovalofscoreinformationalsoaffectedtheuseofotherkindsofinformation

inparticipants’imitationstrategies;however,ratherthanstrengtheningsocially‐mediated

informationbiases(assuggestedbyAbrahamsonandRosenkopf(1997)andGibbons

(2004))suchasfrequencybiasorsimilaritybias,participantsactuallyshowedweakened

oroppositeinclinations.Theaboveinterpretationintermsofchangingthemagnitudeof

movementsintheproblemspaceholdshereaswell.Copyingasimilarsolutiontoyourown

isaninherentlyincrementaliststrategy,sothepresenceofthisbiasinthevisible‐scores

condition,andthepresenceofitsoppositeintheinvisible‐scoresconditioncanalsobe

explainedintermsofanoverallchangefromincrementalisttosaltationiststrategies.The

unpopularitybiasandreducedmomentumbiasweobservedmayhaveoccurredbecause

participantsknewthatimitationdecisionswereoftennotbasedonreliableperformance

information,andthusfrequency‐basedbiasesshouldbeavoidedtokeepfromjoining

informationherds(Banerjee,1992),assuggestedbyGiraldeau,Valone,andTempleton

(2002).

5.4.3.Learning?

Changesinstrategyacrossgameordercanbethoughtofaslearningoradaptation

tothetaskoversuccessivegames.Thechangesweobservedacrossgameorderimplythat

strategiesineachconditionwerestrengthenedoverthecourseofthesession.Inthe

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visible‐scorescondition,thedecreasesinInnovationandImitationandincreasein

Retentionshowamoreincrementalistapproach,whileintheinvisible‐scorescondition,

theincreasesinImitationandRetrievalanddecreaseinInnovationdisplayedmoresolidly

saltationisttendencies.Itisfairlysimpletoseethatanincreasinglyincrementaliststrategy

thatincludedsomeImitationwouldshowanincreasingpayoffintermsofbeingableto

distinguishgoodindividualelementsandpairs,andtheimprovementinscoreacrossgame

orderinthevisible‐scoresconditionreflectsthis.Anincreasinglysaltationiststrategy,

however,isnotlikelytoshowbenefitsunlessthesolutionsofone’speersimprove,and

thuswesawnoimprovementinscoreacrossgameorderintheinvisible‐scorescondition.

Thereisnoobviousbetter‐performingstrategyinthiscontext,however,soparticipants

seeminglydoubleddownonthisone.

5.4.4.Convergent/locallyefficientsearch

Asseenintheincreasingscoreanddecreasingguessdiversitytrendsacrossrounds,

averageperformanceincreasedviatheconvergenceofgroupmembersonregionsofthe

problemspacethatcontainedhigh‐qualityteams.Thisconvergencecombinedwithasmall

amountofindividualexplorationcausedsuchregionstobeexploredmorethoroughlyand

stillbettersolutionstobefound.However,intheinvisible‐scorescondition,whenimitation

wasnotfocusedonasmallgroupofbetter‐performingneighbors(becauseperformance

informationwasnotavailable),similarguesses,orpopularsolutionelements,this

convergencehappenedmuchmoreslowly,searchwasmorediffuseandlessefficient,and

lowerperformanceresulted.Theweakertrendsofincreasingscoreanddecreasingguess

diversityacrossgroupsizeintheinvisible‐scoresconditionshowedthatthelackofscore

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informationmadesearchersunabletoeffectivelytakeadvantageoftheincreasingnumbers

oftheirfellowsearchers.

5.4.5.Cumulativemutualimprovement

Thesignificantcorrelationofimprovementsharewithmeanscoresintheinvisible‐

scoresconditionsshowsthatindividualswhowererelativelymoreskillful(orlucky)were

rewardedwithproportionatelybetteroverallscorescomparedtoothers;thiswasbecause

theirfellowplayerscouldnoteasilycopytheirimprovementsandachievetheirscores,and

becauseknowingthatImitationwasunreliablemadesomeparticipantsmorelikelytoseek

outimprovementsontheirown.Inthevisible‐scoresconditionthiscorrelation

disappeared,butthemoreequitabledistributionofimprovementsshowedthatmore

participantswerecontributingtotheirdiscovery,andmeanscoresincreasedsignificantly

suchthatnearlyallparticipantsdidbetter.Inotherwords,whensociallearningwas

unimpededinthevisible‐scorescondition,highandlowindividualachievershad

approximatelythesamepayoffs,butabsolutepayoffswerehigherforallcomparedtothe

invisible‐scorescondition,inwhichhigh‐achieversgotabiggerpieceofasmallerpie.Thus

impedingsociallearningledtorelativelygreaterinequityandinefficiency,andpresumably

lowerlong‐termperformance(thoughwedidnottestthisexplicitlywithlongergames).

Thisadvantageformoreefficientsociallearningaccruedbecauseimitatorswerenot

merelyscroungers;thesubstantialproportionofImitationpresentinimprovementsshows

thatimitatedguesseswereoftenthebasisforfurthercumulativeinnovations.The

cumulativeinnovationhypothesisissupportedbythefactthatalargerproportionof

improvementsweretheresultofmutualImitationinthevisible‐scorescondition,inwhich

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solutionelementswerepassedbetweenplayersviacopyingandbuiltintobettersolutions

intheprocess.Thisenabledamoreactivesharingofthe“labor”ofproducing

improvements,andincreasedperformancefromparticipantsoverall.Intheinvisible‐

scorescondition,thenecessityofadoptingothers’guessesinordertoobtaininformation

abouttheirperformanceallowedfeweropportunitiestoevaluatevariationsonthem;it

alsopreventedgroupmembersfromperformingthe“filtering”functionofcopyingand

consistentlyretainingonlysolutionelementsassociatedwithrelativelyhighscores,sothat

otherswouldhavelesschanceofobtaininglow‐scoringsolutionelementswhencopying.

5.5.Conclusions

InExperiment2,wenotedthelackofa“tragic”outcomeintheproductionanduse

ofhigh‐scoringsolutions,despitetheapparentincentiveforindividualstounder‐produce

innovationsandfree‐rideontheinnovationsofothersviaself‐interestedimitation.Inthis

experiment,weshowedthatitwaspossibletoinduceatragicoutcomebyreducingthe

capacityofindividualstomakeself‐interestedimitationdecisions,evenwhilethey

increasedtheirproductionofinnovation.

Itappearsthatlowerperformanceinthistaskwasnotduetoanunderprovisionof

individualinnovation,butalackofevaluativefilteringofsolutionelements,which

participantsinthevisible‐scoresconditiondidbychoosingtoimitateandretainsolution

elementsassociatedwithhighscores,andwhichinthescores‐invisibleconditionwasmade

muchmoredifficult.Theconsistentuseofthebetter‐performingsolutionsdoesnotrelyon

altruisticorpublicly‐mindedmotives,butsuchfilteringisimportantforsupportingothers'

successfulsociallearning,aswashighlightedinarecenttournamentofsimulatedsocial

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learningstrategies(Rendellet.al2010).Insummary,wehaveshownthroughthis

experimentthatwhenknowledgeiscumulative,efficientandinformedappropriationisan

importantstepinfurtherprovisionofthepublicgoodofknowledge.

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6.KnowledgeasProperty

6.1.Promotingprogress

Intwopartsofthesociallearningexperimentsdescribedthusfar(largergroup

sizesinExperiment1,andthescores‐invisibleconditioninExperiment3),wehaveseen

thatdespiteapparentlyadequateprovisionofinnovation,obstaclestoaccurate,strategic

imitationofthoseinnovationscanleadtounderperformanceinfurtherinnovation.Inthis

chapterwewillexploresomemeasurestakenintherealworldto(ostensibly)encourage

efficientinnovationand(eventual)imitation,andintroduceseveralimportantconceptsfor

understandingtheirimplicationsontherelatedpublicandcommongoodsofknowledge

discussedinChapter4.

6.1.1.TheProgressClause

Practicalresearchanddevelopmentarecostlyactivitiesintermsofmoney,effort,

time,risk,andopportunity.Theseactivitiesgenerallywillnotbeundertakenunlesstheir

resultshavesomeexpectedvaluetojustifytheircosts.The"ProgressClause"oftheU.S.

Constitutionempowersthelegislature"TopromotetheProgressofScienceandusefulArts,

bysecuringforlimitedTimestoAuthorsandInventorstheexclusiveRighttotheir

respectiveWritingsandDiscoveries."Manyothercountrieshaveenactedsimilarstatutes

andpoliciesprotecting"intellectualproperty"(IP),whichgenerallyallowtheoriginatorsof

certaininnovationstocontrolthedisseminationorproduction(andthusthebenefit)ofthe

productsoftheirinnovations.(Thisclausecoversthecreationofbothpatentsand

copyrights;inthischapterandthenext,wewillbefocusingonpatents,thoughmanyofthe

sameargumentscouldapplytocopyrights.)TheownerofapatentgrantedbytheU.S.

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PatentandTrademarkOfficeisgiventherighttoexcludeothersfrom"making,using,

selling,offeringtosell,orimporting"thepatentedinvention(35U.S.C.§271),andthisright

canbereneweduntil20yearsafterthepatentapplicationwasfiled(35U.S.C.§154).In

exchange,apatentapplicantmustdescribetheinventioninenoughdetailsothataperson

whoisskilledinthefieldwouldbeabletomakeandusetheinvention(35U.S.C.§112).

Thedisclosurerequiredforapatentedinventioncanbeconsideredacontribution

toaknowledgecommons,inthattheinformationthatenablesoneto"makeanduse"the

inventioncanalsobeusedtoimproveit,ortocreateotherinventions.AsGhosh(2003)

notes,thecharacterizationofagoodasrivalrousdependsonthepropertyrightsthat

governit.TheexclusivecontroloveraninventionthatIPstatutesgivetocreatorscanmake

thatinventionusablebyonlyoneindividualorfirm,andsoartificiallytransformpractical

knowledgeintoasubtractableresource.ThustheexerciseofIPrightscanbeconsidered

appropriationofresourceunitsfromthecommons,whichcannotbedoneinan

unrestrainedwaywithoutthreateningtheviabilityoftheresource.

Thebalanceofrightsandresponsibilitiesintheseprovisionsimplicitly

acknowledgesthatindividualinnovationisencouragedforthepurposeoftheextending

thecollectivebenefitsofthegeneralprogressofknowledge.Thestandardassumption

abouttheintentofthe"ProgressClause"isthatitwasmotivatedbytheframers'viewthat

"encouragementofindividualeffortbypersonalgainisthebestwaytoadvancepublic

welfare"(MazervStein,1954).Thatis,publicbenefitistheprimaryintendedend,andthe

provisionofaprivateincentiveisthepreferredmeansforachievingit.Asdiscussed

previously,however,privatizationofaresourceisnotalwaysthebestwayofensuringits

equitable,efficient,andsustainableuse.

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6.1.2.Measuringthepromotionofprogress

Theprogressofsciencedependsontheincentivesthatinventorshavetoinvestin

researchanddevelopment,aswellastodisseminatetheirinventionstothosewhocan

productivelyadopttheminsocietyatlarge.Thus,thesuccessofpatentstatutesinthe

promotionofscientificprogresscanbeusefullyevaluatedonthebasisoftheneteffectsof

theIPsystem,bothforthosewhodirectlyadvancetheprogressofscience,andforthe

generalpopulace.Thereareundoubtedlybenefitsthataccruetomanypatentholdersasa

resultoftheirexchangeofideasformoney,asthereareplainlybenefitstosocietyinthe

formofpatentedmoderntechnologies.ThequestioniswhethertherewardsoftheIP

systemoutweighitscostsforallinventors(boththosewhoareIPholdersandthosewhose

inventionsarenotprotectedbyIP),andthesocietyandeconomyinwhichtheywork.(The

lattercanbeconsideredanextensionoftheformer:aseconomiesandsocietiesgrow,new

technologicalneedsariseandthusnewopportunitiesforinnovation.)Herewewilltakea

shortdetourtoexaminepreviousattemptstoanswerthisquestionempirically,aswellas

thetheoriesunderlyingIPsystems;thesewillhelpconstrainandmotivateourfinal

experiment.

Though"rights"canseemratherabstract,proxieshavebeendevelopedforstudying

thequantitativeeffectsofvariousfactorsonoveralleconomicgrowthincross‐national

econometricstudies,includingprotectionsforpropertyrights.Generally,traditional

propertyrights(thosegoverninge.g.objectsorrealestate)haveastrongandunambiguous

relationshipwithgrowth(Svejnar,2002;Keefer&Knack,1995,1997).ParkandGinarte

(1997)performedaregressionusingindicesof"marketfreedom"(i.e.traditionalproperty

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rights)aswellasIPrights,andconfirmedthattheformerhadastrongrelationshipwith

growth,butnotthelatter.Inafollow‐upstudy,GinarteandPark(1997)actuallyfound

evidenceforacorrelationbetween5‐yearlaggedR&DspendingandthestrengthofIP

rightsprotection,implyingthatinvestmentininnovationsledtothedevelopmentof

protectionsforthem("reversecausality").Incontrasttotraditionalpropertyrights,IP

rightsappeartohaveonlyanindirectorweakrelationshiptoeconomicgrowth;itmay

holdonlyforcertaingroupsofcountriesorcertainkindsofmeasures(Falvey,Foster,and

Greenaway,2006),andthecausaldirectionisunclear.

SeverallinesofresearchhavebeenpursuedtoaddressthequestionofwhetherIP

rightsarebeneficialforinventors(andtheiremployersandinvestors).Studiesof

innovationpriortoandduringthe19thcenturyshowedthatmanyinventionsmadetheir

inventorsenormousprofitsandwerejudgedtobehighlyinnovativedespitebeing

unpatentedorhavingtheirpatentsinvalidated(Mokyr,1999;Moser,2002).Bessenand

Meurer(2008)andBoldrinandLevine(2008)reviewedabroadrangeof"natural

economicexperiments"ondiscretechangesinthepatentlawsofvariouscountriesinthe

20thcentury.Theyfoundthat,overall,thereisstrongevidencethatstrengtheningpatent

protectionleadstomorepatenting(asinthe"reversecausality"notedabove),butweakor

noevidencethatitincreasesinnovation.Infact,intherealmofsoftwarepatents,firmsthat

acquiredrelativelymorepatentssubsequentlytendedtoreducetheirR&Dspending

relativetosales(Bessen&Hunt,2007).BoldrinandLevine(2008)describeincreasesin

patentingactivityas"navigatingthepatentthickets,"inwhichfirmsthatfearinfringement

lawsuitsfromas‐yet‐unknownpatenteesacquirepatentsstrictlyforthepurposeoffiling

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countersuitsandachievingsettlementswithouthavingtomodifytheirbusiness,thatis,to

avoidbeingforcedtoinnovatefurther.

BessenandMeurer(2008)examinedpatentrenewalbehaviorinordertoestimate

thevalueofpatentsapartfromtheirunderlyingtechnologies,andfoundthatnearly60%of

U.S.patentsfiledin1991werenotrenewedtofullterm,whichindicatesthatthemajority

ofpatentsfileddepreciatetoavaluelessthanthefewthousanddollarsoftheaverage

renewalfee.Asonemightexpect,thedistributionofpatentvaluesisskewed‐‐most

patentsareofrelativelylittlevalue,whileasmallnumberarequitevaluable.Avarietyof

measuresofpatentandinventionvalueadhereapproximatelytothe80‐20rule:80percent

ofthetotalvalueiscontainedin20percentoftheinventions(Harhoff,Scherer,&Vopel,

2003).BessenandMeurer(2005)foundthatgenerally,patentsgrantedtosmallinventors

(individuals,nonprofitsandcorporationswithlessthan500employees)aremuchless

valuablethanthosegrantedtolargerentities,about50%inthemean,andthedifference

betweenindividualsandorganizationsoverallisevengreater.Furthermore,theownership

ofthisvalueisfoundtoberatherlopsided:morethanhalfofthevalueofworldwide

patentsaccruestoasmallnumberoflargepharmaceuticalcompanies,andmorethantwo‐

thirdstofirmsinthechemicalandpharmaceuticalindustriesgenerally.

Overall,thereisstrongevidencethatpatentscandeliversignificantvalueto(some

of)theirowners,butthepatentsystemalsoimposescostsonpatentownersthrough

disputesovertherightstotheirinventions,aswellasonnonpatentinginventorsthrough

disputesrelatedtoinadvertentinfringementofothers'patents.Theprocessof"clearing"

rights(byeithermakingsurenotrespassoccursorobtainingalicense)isnotnecessarily

simpleformanypatents,becausetheboundariesofwhataninventiondoes,andbywhat

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processormethoditisdone,canbearcaneandopentocostlylegalinterpretation(Moore,

2005).BessenandMeurer(2005),aftercontrollingforawidevarietyofvariables,found

thatincreasedspendingonR&Disactuallycorrelatedwithanincreasedriskofbeingsued

forinfringement,whichsuggeststhatinfringementisoftennotwillful,andoccursdueto

difficultiesindeterminingpatentboundaries.Acomparisonofaggregatelitigationlosses

incurredbyasampleofdefendantpublicfirmsduringtheyearsof1984‐1999withthe

aggregateincrementalprofitsderivedbypublicfirmsduringthesameperiodshowedthat

outsideofthechemicalandpharmaceuticalindustries,thecostsoflitigationclearly

exceededprofitsfrompatents(Bessen&Meurer,2008).Thusoverall,thepatentsystem

appearstoconstituteanetdisincentiveforinnovation.

Theresultsnotedabovesuggestthatinitspresentform,thepatentsystemisnot

promotingtheprogressoftechnologicaladvancement;thatis,theequity,efficiency,and

sustainabilityoftheknowledgecommonsdonotappeartobeimprovedbythepatent

system.Thismaysimplybeduetostructuralshortcomingsofthesystem,remediableby

adjustmentstopatentlengthorbreadth(Gilbert&Shapiro,1990).However,theremay

alsobemoresubtleissuesregardingthemotivationalprinciplesandinterdependenciesof

innovatorsthatarenotbeingadequatelyaddressedbyexistingpatenttheory,law,and

institutions.

6.2.Prospectingforprogress

Themonopolygrantedbyapatentisexpectedtocause"deadweightloss,"a

reductioninmutualvalueforproducersandconsumersthatoccurswhenconsumerswho

arewillingtopaymorethanthemarginalproductioncostofagood,butlessthanthe

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patentee'smonopolyprice,arethuspreventedfrompurchasingthegood(Gilbert&

Shapiro,1990).Kitch(1977)introducedthe"prospecttheory"ofpatentstocommonlegal

usage,inwhichthecosttosocietyofdeadweightlossisexplicitlyjustifiedanddiscounted

byaperceivedneedtoincentivizenotjustcreationanddisclosureofinnovations,butalso

theirefficientmanagement.Kitchexpoundeduponthistheorywithananalogytothe

exploitationofmineralresourcesintheAmericanWest,buthewasrespondingtoBarzel's

(1968)callforasolutiontoacollectiveactionproblemamonginnovators.Barzelobserved

thatfirmswhowantedtousethe"freepublicgood"ofbasicscientificknowledgeto

produceinnovationsforcommercialuseeachhadanincentivetointroducesuch

innovationsassoonastheywereprofitable.Buthereasonedthatinnovators(andthus

societyatlarge)wouldcollectivelybebetteroffiffirmsdelayedtheintroductionof

innovationsuntilan"optimal"time,whenmarginalprofit(relativetoreliableoutside

investments)couldbemaximizedthroughthedevelopmentofsufficientproduction

capacityanddemand.InthesameyearasHardin's(1968)analysisoftheTragedyofthe

Commons,Barzel(1968)alsorecommendedenclosureoftheknowledgecommonsinthe

formofownershipofbasicknowledgeinordertopreventwhatheviewedasatragic

outcomeinitsuse.ButaswithHardin,theintellectualorigins,analogies,andassumptions

usedtounderstandthiscomplexsituationmustbecloselyexaminedforcluesastowhere

proposedsolutionsmaysucceedorfail.

Barzel'sanalysisofthis"optimal"usedependsonanumberofsimplifying

assumptions;forourpurposesthemostsalientarethat(a)innovationshaveaconstant

costandthuscanbeintroducedatanytime(ignoringthedynamicandcumulative

developmentofknowledge),(b)thereisonlyoneinnovatorassociatedwithagiven

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innovation(ignoringcollaborativeinnovationprocesses),(c)therearenobenefitsofthe

innovationpassedontotheconsumer(ignoringtheexistenceofexternalitiesor

"spillovers"(Frischmann&Lemley,2007)uncapturablebytheproducer,suchas"network

effects"(Katz&Shapiro,1985)),and(d)theparametersofthesystemarewidelyand

accuratelyknown(ignoringthecomplexanduncertainnatureofinnovation).Kitch(1977)

argued,amongotherthings,thattheU.S.patentsystemwasstructurallypredisposedto

"prospect"uses,andthatgrantingbroadandlong‐termpatentrightsonthebasisofthe

"prospect"forefficientintroductionandmanagementofaninnovation(ratherthanonthe

basisofthepreviously‐accepted"rewardtheory"ofsimplyincentivizingproductionand

disclosureofinnovations)wouldresultinanetpositiveforsociety.

Implicitinthisapproachareotherassumptionsaboutinnovatorsandtheir

motivations.Primarily,theaboveanalysestreatinnovationasanactivitythatispursued

onlybyfirmswhoproducegoodsforthepurposeofsellingthemtoendusers.Themining

analogyusedbyKitch(1977)impliesthatmostpracticalinventionsrequireagreatdealof

investmentintheextractionandprocessingofthe"ore"ofbasicknowledge,andthusthat

firmswithexclusiveclaimswillbethebestinformedandequippedtocreateandmanage

innovations.However,thehistoryoftechnologyshouldteachusthatpeoplearegenerally

notskilledatanticipatingtheusesofnewinventionsortheneedsoffutureusers(Boyle,

2007);inventionssuchasmobilephones,DVDplayers,andfinancialdatabasesoftware

haveresultedinavarietyofusesandamagnitudeofeconomicandsocialbenefits

unimaginableanduncapturablebytheircreators(Baumol,2002).Thoughprospecttheory

positsadecentralized,entrepreneurialimplementationofinnovationatlarge,itcentralizes

controlofanyparticularinnovationinonefirm.Inpractice,holdersofpatentscandelayor

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preventfutureinnovationsbyeitherrefusingtolicensetheirpatentstosubsequent

innovators,orchargingsufficientlyhighlicensingfeessothatsmallerinnovatorsare

preventedfromenteringthemarket(Merges&Nelson,1990).

Previousinventionscanaidinthecreationofnewinnovationseitheras“research

tools”thatenableafurtherinnovativestage,orasthebasisforanimprovedproduct(or

sequentialinnovation)onthe“qualityladder”(Hall,2007).Itisnotnecessarilythecase

thateithertheoriginalinnovatororonlythosewithdeep‐pocketedinvestorsarebest

suitedtoimproveuponoruseapreviousinnovationtocreateanother,butinsomecases

thesemaybetheonlyagentswhoareabletodoso.Additionally,innovatorsmaynothave

sufficientincentivetocreateorallowimprovementsontheiroriginalideas,iftheyfearthat

anewusewouldcompetewiththeoldone(Scotchmer,1991).Whenpreviousinnovations

necessaryforthecreationordevelopmentofanewinventionarepatentedbymultiple

parties,aphenomenoncalled“thetragedyoftheanticommons”canresult(Heller&

Eisenberg,1998).Inthissituation,thetragedyresultsnotfromalackofresourceoversight,

butfromanexcessofit;ownersoftechnologiesthatarecollectivelynecessaryforanew

innovationmayfailtoagreeonlicensingorrevenuesharingterms,andthusanyofthem

canvetofurtherprogress.

Tosummarize,wehaveseenthatpatentsystemsareintendedtoincentivizethe

creationanddisclosureofinnovations,aswellastheirefficientmanagement(undercertain

interpretations).Inpractice,however,patentscanalso(a)incentivizenon‐innovative

strategicorrent‐seekingbehavior,(b)reducetheincentivestocreateanddisclosethrough

theaccompanyingriskofcostlypatentlitigation,and(c)reducetheincentivetooptimally

managethroughpatentholders'abilitytodelayorprevent(butnotcaptureorprofitfrom)

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manypositiveexternalitiesoftheirpatentedinnovations.Theabovefactorsalsoconstitute

disincentivestoimitateandbuildsequentialimprovementsfromtheinnovationsofothers.

Returningtotheconceptofaknowledgecommons,theseproblemsaresignsofan

institutionwhichisfailingtoensurecontributionandpreventoverappropriationfroma

resource(theoverallpoolofexistingknowledge)byitscommunityofusers.Inthelong

term,suchflawsthreatentheviabilityoftheresource.

6.3.Balancingmotivations

Anotherareaofresearchinwhichtheadequacyofexclusioninfosteringinnovation

becomessuspectisthecurioustendencyofpeopletotreatextrinsicincentives(suchas

monetarypayment)andintrinsicorsocialmotivations(suchaspersonalsatisfactionor

socialapprobation)differently:asnon‐additive,mutuallyexclusive,orcompletely

incommensurable.Forexample,givenanactivitythatproducesintrinsicrewardssuchas

volunteerserviceorblooddonation,theofferofmonetaryrewardsmayactually"crowd

out"themotivationtopursuetheactivityandreduceitsoveralllevel.Thus,undercertain

circumstancesthepricemechanismforraisingthesupplyofgoods,oneofthefundamental

pillarsofeconomics,maynothold.Thestudyofthisphenomenonhasproducedalarge

bodyofworkinbotheconomics(e.g.Titmuss,1970;Frey&Jegen,2001)andsocial

psychology(e.g.Deci,1971;Deci,Koestner&Ryan,1999).

HeymanandAriely(2004)positedthatsocialandmonetaryrewardsaremediated

byseparate"markets,”andthattheycannotbemixed.Theyperformedexperimentsin

whichtheymeasuredtheeffortputforthinresponsetovaryinglevelsandtypesofrewards

offeredtoparticipantsforperformanceofatask.Itwasfoundthateffortwasconsistently

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highwhennorewardwasoffered,aswellaswhentokennon‐monetaryrewards(e.g.

candy)ofvaryingvaluewereoffered.Whencashwasofferedorthecashvalueofthenon‐

monetaryrewardswasmentioned,effortwasproportionaltothevalueofthereward

offered,andonlyapproachedthelevelreachedbynorewardsathighlevelsofmonetary

rewards.

FreyandJegen(2001)reviewedstudiesrelatedtothecrowding‐outeffectof

extrinsicrewardsonintrinsicmotivationsandfoundthatitwaspresentforavarietyof

norm‐relatedmotivationsandsettings:workeffortandreciprocityinsupplyinglabor,

altruisminserviceprovision,civicdutyandenvironmentalcareinmanagingacommon‐

poolresource,andtrustinlegalsystems.Deci,Koestner,andRyan(1999)performeda

meta‐analysisof128studiesonthiseffectandfoundthatawidevarietyofextrinsic

rewardsandrewardcriteriaunderminedintrinsicmotivationandinterestineffortful

tasks.

Thepresenceofsocialorintrinsicrewardsforsomecreativeandinnovativeactivity

isinasenseevidentbydefinition,fromthefactthatsuchbehaviorscontinueinamultitude

ofcontextswithoutanyexternalmonetaryreward,andeveninthepresenceofsubstantial

costs(e.g.varioushobbyistpursuits,amateurblogging,Wikipediacontributions,etc.)

Beyondthisevidence,theintrinsicmotivationsthatpeoplehaveforcreativeworkhave

alsobeenstudiedinsomedetailandavarietyofreasonsarefoundforparticipating:

curiosity,theenjoymentofchallengeornovelty,personalexpressionofvalues,buildingor

maintainingapositivereputationamongpeers,andsoforth(Lakhani&Wolf,2003).

Totheextentthatinnovatorsunderstandthedependenceoftheirworkonthatof

previousinnovators,andthatspilloverscanaccruetofellowinnovatorsandtosocietyat

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largeasaresultoftheirefforts,themotivationsofreciprocityandpublicbenefitsmaybe

includedinthislistofintrinsicmotivations.Inthiscase,theopportunitytoexcludeothers

frombuildinguponone'sworkmaybeunattractive.Totheextentthatextrinsicrewards

canunderminethesemotivationsforcertainkindsofwork,someinnovativeactivitymay

simplynotoccur,oronlyatagreaterrelativecost.

6.4.Othermodelsofinnovation

Theseflawspromptustoconsiderothermodelsofinnovationanditsgovernance.

Theassumptionsofthe"reward"and"prospect"theoriesofinnovationbyproducers

excludeimportantclassesofinnovators:individualsorfirmswhocreateinnovationsfor

theirowninternaluse,andthosewhoproduceinnovationsinopencollaborationwith

othersinordertoshareinthecostsoftheircreationandthebenefitsoftheiruse(Baldwin

&vonHippel,2009;Strandburg,2009).

Innovationscreatedbyindividualsorfirmsfortheirowninternaluse(ratherthan

forsellingtousersataprofit)needonlytoprovideenoughbenefittocovertheeffortof

producingthem.Thismeansthatsmall,incremental,orspecializedinnovationsthatmight

notjustifyinvestmentorproductionbyanon‐userfirmcanbecreatedwithoutthe

provisionofexternalincentives.Studiesinawidevarietyofindustriessuchaschemical

products(Freeman,1968),scientificinstrumentsandsemiconductors(VonHippel,1976,

1977),andsportingequipment(Shah,2000)haveshownthatalargeproportionof

importantandnovelproductsandprocessesweredevelopedbyusers,andthatsubstantial

proportionsofusersengageindevelopingormodifyingproductstheyuse(Gault&von

Hippel,2009).Moreover,userinnovatorsoften"freelyreveal"(relinquishexclusiverights

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andallowgeneralaccessto)theirinnovations(Harhoff,Henkel,&vonHippel,2003).They

dothisbothtoavoidthecostsanddifficultyofexcludingothersthroughIPrights(as

discussedabove)ortradesecrecy,andtotakeadvantageofprivatebenefitssuchasaccess

tothesequentialimprovementsofothers,reputationenhancement,orpositivenetwork

effectsresultingfromincreaseduseoftheirinnovation(Harhoff,Henkel,&vonHippel,

2003).However,userinnovatorscanalsomaintainsomeIPrightsandpursueotherlegal

measuresforthepurposeofavoidingexpropriationoftheirefforts(O'Mahony,2003).

Thisconceptcanbetakentoanotherlevelinopencollaborativeinnovation,in

whichagroupofusersactivelyrevealandcoordinatetheircreativecontributionstoeach

otherforintegrationinalarger‐scaleproject,effectivelypoolingtheirinvestmentswith

assurancesthatallwillshareintherewards.Suchprocessesareinusemostrecentlyand

visiblyinopen‐sourcesoftwaredevelopment(Benkler,2002),butthismodelof

developmenthasbeenusedinotherindustriesformanyyears(Allen,1983).Open‐source

contributorsdosobecausetheywanttoincluderatherthanexcludeothersfromtheuseof

theircontributions,oftenfornormativereasonsrelatedtothecultureofopen‐source

software,orforprivatebenefitssuchasthosementionedabove(Lerner,Tirole,&Pathak,

2006).Advancesincomputingpowerhaveenabledlargereductionsindesignand

developmentcostsforuserinnovation,andrelatedadvancesinnetworkedcommunication

andcollaborationsoftwarehaveloweredbarriersforthecoordinationofcontributionsin

collaborativeprojects(Benkler,2002).Thesedevelopments,alongwiththeincentivesthat

suchactivitiesprovideforbothinnovationandimitation(andrelatedsequential

innovationsandotherspillovers),makeitincreasinglyattractiveasamodeofscientificand

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generalacademicpractice(Boyle,2007;Lougee,2007),aswellasmoresociallyoptimal

governanceofknowledge(Baldwin&vonHippel,2009).

6.5.Testingmodelsofincentivesandprogress

ThecomplexityofIPsystemsaswellastheirlargepotentialimpactoneconomic,

technological,andculturaloutcomesinsocietymakesthemfertilebreedinggroundsfor

theoriesaboutunderlyingissuessuchasincentives,conformity,creativity,theoptimal

balancingofindividualandcommoninterests,thenatureandstructureofknowledge,and

ahostofotherissues;thesetheoriesbynecessitycrossdisciplinaryboundariesoflaw,

politicalscience,economics,psychology,andphilosophy.Thepurposeofexperimentsin

understanding"intellectualproperty"andthepromotionofintellectualdiscovery,asinany

othersystem,istosimplifytheissuesathandinordertoshowmoreclearlyhowthey

operateandinteract,andinsodoing,topointoutwhatisnotwellunderstoodforfurther

study.

Thepreviousexperimentsinthisdissertationcanbeconceptuallycomparedtoopen

collaborativedevelopment,becauseeveryparticipant'scandidatesolutionsand(exceptin

onecondition)informationabouttheirperformanceareavailableforusebyothersinthe

group,withnocostorhindrance(thoughparticipantsdidnothaveachoiceinthematter).

However,therewardsforgoodandbadperformancearemateriallythesame‐‐course

creditwastheonlycompensationgiventoallparticipants.Wewishedtotesttheeffectofa

changetotheincentivesinthiscontextbypayingparticipantsasmallcashrewardbased

ontheirperformance,aswellasimplementingaverybasicandlimitedpatent‐likesystem.

Inthissystem,eachparticipantwouldbeallowed,atacertaincostandforalimitedtime,to

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automaticallychargeotherswhocopytheirinnovations.Thepreviouslyexistingincentives

forinnovation(thepossibilityofreceivingthebenefitofanimprovedsolution)wouldbe

enhancedbythepaymentsthatsuccessfulinnovatorscouldgetfortheirsolutions;the

previouslyexistingincentivesforimitationwouldbereducedbythepaymenttothe

imitatedplayer.

Thischangewouldostensiblyincreasetheuseofinnovation,whichcouldresultin

thediscoveryofbettersolutions,whichcouldbecopiedbyotheruserswhilerewarding

originators.Butweknowfrompreviousexperimentsthatinnovationisrisky,andthegains

ofimprovementscanbecanceledoutbypoorer‐performingsolutionsdiscoveredinthe

process.Wealsoknowfromtheseexperimentsthatcumulativeimprovementsare

importanttothecollectiveperformanceofgroups‐‐ifthischangecausedlessefficient

imitationorlessuseofimitationoverall,thegainsachievedbysuccessfulinnovatorscould

failtopropagateandbearfruitinsequentialimprovements.Thereisalsotheriskthat

competitivemotivationsamongparticipantscouldleadtoexcessivepatentingto

intentionallykeepothersfromimitation,withoutregardtopotentialinnovatorgainsvia

transfersfromimitators.

Previouslaboratoryexperimentsbyothersregardingtheconsequencesofdifferent

systemsfordistributingandrewardingknowledgeproductiondonotgiveusreasonfor

confidenceintheperformanceofexclusionarypatentsystems.Onesuchstudycompared

"patent‐like”(winner‐take‐all,accordingtofirstdiscoveryofthebestsolutionelements)

and"market‐based"rewardsystems(inwhichparticipantscanbuyandsellsharesin

solutioncomponents,effectivelymakingbetsonthesuccessoftheirsolutions)forgroups

attemptingtosolvetheKnapsackProblem,andshowedsubstantiallyinferiorperformance

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forthepatent‐likesystem(Meloso,Copic,&Bossaerts,2009).Anotherexperimentusinga

multi‐userinventiongametaskshowedthatboth“patent‐only”andmixed"patentand

commons"systemsofcumulativeinventionunderperformeda"commons‐only"systemon

severalmeasures,includinginnovation,productivity,andsocietalutility(Torrance&

Tomlinson,2009).

Wewilldiscusstheseexperimentsfurtherinthenextchapterincomparisonwith

ourownresultsinExperiment4.Inthisexperiment,wehavenotattemptedtoapproach

thelevelofversimilitudetorealpatentsystemsseenintheabovementionedstudies,

becauseweareinterestedintheeffectsofchangingincentivesongeneralizedsearchtasks,

andnotnecessarilyinallofthespecificdetailsofaparticularpotentialpatentsystem.We

expectthattheresultsofthisexperimentwillhavesomerelevancetopatentsystems,as

wellasothersituationsinwhichenvironmentalorinstitutionalfactorschangethe

incentivesofthosewhoexplore.ThegoalsforExperiment4aretocontinueourstudyof

thebasicmechanicsanddynamicsofsociallearningseeninthepreviousexperiments,by

examininghowtheyareinfluencedbyconcreteanddifferentialrewardsfordifferent

searchstrategies,andhowindividual‐levelprocessesaffectgroup‐levelresults.

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7.Experiment4–CreatureGameC(paymentandprotection)

7.1.Experiment4Overview

ThetaskusedinthisexperimentwasthesameasinExperiment3,withfourmajor

changes:(1)inhalfofthegamesineachexperimentsession,weallowedparticipantsto

forfeitasmallnumberofpointsto“protect”theirguessessothatotherswhousedthesame

guess(oranyverysimilarguess)wereforcedtopayasmallnumberofpointstothe

protector;(2)welengthenedthetimeofeachroundslightly,sothatparticipantswould

havesufficienttimetotakenoteofwhethertheirguesswasprotectedbyanotherplayer

andchangeitiftheywished,andthenumberofgamesineachexperimentsessionwas

decreased,inordertofitthesessionintheallottedtime;(3)participantsreceivedasmall

cashpaymentaccordingtothenumberofpointstheyearnedinthegame;(4)participants

filledoutapost‐tasksurveyabouttheirperceptionsofthetask,andtheirownstrategies

andperformance.

Modification(1)allowedfortheexaminationofdifferencesinstrategiesand

performanceassociatedwithchangingtheincentivesforasocialandsociallearning.

Modification(2)wasintendedtoavoidnoiseinthedataassociatedwithunintendedor

hurriedchoices.Modification(3)allowedfortheexaminationofbehavioraldifferences

(frompreviousexperiments)associatedwithextrinsicmonetaryrewards.Modification(4)

offeredfurtherinsightintothemotivationsandjudgmentsofparticipants,whichcouldbe

correlatedwiththeirbehaviorinthetask.

7.1.1.Predictions

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Inthegameswherethe“protection”featurewasunavailable,weexpectedlittle

changeinbehaviorandonlyasmallimprovementinperformance(comparedtothevisible‐

scoresconditionofExperiment3)duetothesmalladditionaltimeperroundandthe

expectationofcashrewards.Whentheprotectionfeaturewasavailable,weexpected

differencesinresultscomparedtowhenitwasnotavailable.Thepossibilityofreceiving

additionalpointsfromimitatorswaspredictedtocauseparticipantstoinnovatemorein

ordertofindrelativelyhighscoringsolutions,andthosewithhighscoringsolutionswould

tendtoprotectthemwhenpossible.Thoughthe“fee”forusingaprotectedsolutionwasset

quitelowrelativetotheaveragescoreearnedinasingleround,weexpectedthat

participantswouldavoidimitatingprotectedsolutions,thusreducingimitationbehavior

overall,anddirectingalargershareofimitationtounprotectedlower‐scoringsolutions.

SimilartoExperiment3,thiswasexpectedtoreduceorreversesociallearningbiasessuch

asfrequencyandsimilaritybias.Thecombinationofthesetwoinfluenceswouldslow

convergenceofsolutions,andkeepguessdiversityrelativelyhigh.Asforperformance,we

expectedthattheextraincentivetoexplorewouldresultinhighermaximumscores,but

thelargenumberoflowerscoresencounteredintheprocess,aswellasthedisincentiveto

builduponthe(protected)bettersolutionsfoundthroughthisincreaseinexploration

wouldlowersearchefficiency,thusmakingmeanperformancethesameorlowerthan

whenprotectionwasunavailable.

7.2.Experiment4Methods

159participantswererecruitedfromtheIndianaUniversityPsychology

Departmentundergraduatesubjectpool,andwereofferedcoursecreditfortakingpartin

147

thestudy,aswellasasmallcashpaymentaccordingtotheirperformance(meanpayment

wasapproximatelythreedollars).Participantspopulatedeachsessionbysigningupatwill

forscheduledexperimentswithamaximumcapacityof9persons,andweredistributed

across45sessionsasshowninTable7.1.Oneparticipant’sdata(fromoneofthe8‐person

sessions)wasexcludedduetoextremelyoutlyingperformance.

Table7.1:DistributionofparticipantsacrossgroupsizesinExperiment3

Groupsize 1 2 3 4 5 6 7 8 9

#Sessions 14 8 3 4 5 4 3 2 2

#Participants 14 16 9 16 25 24 21 16 18

Thetaskusedwasnearlyidenticaltothatofthevisible‐scoresconditionin

Experiment3,withthefollowingchanges.

Protectionavailability:inhalfofthegamesineachsession(theprotectionavailable

orPAcondition),participantswerepresentedwithachoiceforsevensecondsattheendof

eachround(justafterlearningthescoreassociatedwiththeirsolution)toforfeitfour

points(approximately.042intermsofnormalizedscore)to“protect”thesolution(ifthey

madenoselectionwhilethechoicewasavailable,thedefaultwasnottoprotect).Forthe

nextthreeroundsafterasolutionwasprotected,anyotherplayerwhoused(attheendof

theround)asolutionwithinoneelementdifferenceoftheprotectedsolutionwould

automaticallytransfertwopoints(approximately.021innormalizedscore)tothe

protector.Solutionswithinoneelementdifferenceofaprotectedsolutioncouldnotbe

protected.

148

Theprotectionfeeandusefee,respectively,wereintentionallysetatfairlylow

valuesinordertoensurethatthecostfortheseoptionswouldbevisiblebutwouldnot

undulydiscourageparticipantsfromusingthem,orexcessivelywarpincentivestoward

oneoptionortheother.Thewordingoftheoptionspresentedtoparticipantsattheendof

eachroundisshowninAppendix7.A.Weensuredthatparticipantsunderstoodthese

optionswithadditionalinstructionsandhands‐ondemonstrationsbeforedatagathering

began.Inordertoensurethatparticipantswereawareofthedecisionstheymade

concerningtheuseofprotectedteamsduringeachround,anypeers’teamsthatwere

currentlyprotectedwereshownwiththeirbackgroundhighlightedinbrightred.In

addition,whenaparticipantchangedtheirteamsuchthatitwasprotectedbyanother

player,itsbackgroundwasalsohighlightedinbrightred,andthemessage“Protectedby

anotherplayer”wasshownaboveit(thesenotificationsoccurredassoonasthechange

wasmade,notattheendoftheround).Ineachround,werecordedwhethereach

participantprotectedhisorherteamorusedanother’sprotectedteam,andhowmany

others(ifany)usedtheplayer’sprotectedteam.Intheotherhalfofthegamesineach

session(theprotectionunavailableorPUcondition),theprotectionoptionwasnot

availabletoparticipants,andgameswereplayedastheywereintheScoresVisible

conditionfromExperiment3.Gameswereplayedinarandomorderineachsession.

Longerroundsandfewergames:togiveparticipantssufficienttimetoevaluatethis

choiceandchangetheirguessesifdesiredintheprotectionavailablecondition,andtobe

abletoproperlycomparebehaviorbetweenconditions,welengthenedeachroundfrom10

to15secondsinbothconditions.Becauseofthelongerrounds(includingtheadditional

secondsgiventomaketheprotectionchoiceaftereachround),additionalpracticetimefor

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thenewgamefeatures,andthepost‐tasksurvey(discussedbelow),wereducedthe

numberofgamesineachexperimentsessionfromsixtofourtofitthesessionintheone‐

hourtimelimitrequiredforexperimentsusingoursubjectpool.Ofcourse,thedistinction

betweengamesintheprotectionavailableandprotectionunavailableconditionsonly

matteredinsessionsthatincludedmorethanoneparticipant,butroundsandsessions

wereidenticalinlengthforallparticipantgroupsizes.

Payment:participantswereinformedbeforeeachsessionthattheywouldreceivea

smallcashpaymentof“afewdollars”whichwouldvaryaccordingtothetotalnumberof

pointstheyearnedindividuallyduringthesession.Wesetthepaymentperpoint

($0.00086)accordingtothedistributionofscoresfromExperiment3,suchthatthemean

paymentwouldbeapproximately$3.00.

Post­tasksurvey:wedeviseda10‐itemquestionnaireforparticipantstocomplete

afterthefinalgameineachsessioninordertogatherself‐reportdataonparticipants’

attitudesandjudgmentsaboutthetaskandtheirstrategies,whichincluded8multiple‐

choicequestionswithresponseoptionsonaLikertscale,andtwofree‐responseitems.The

fulltextofthesurveyisshowninAppendix7.B.

Thedistributionofindividualpointvaluesandinteractionsfortheiconswasthe

sameasinExperiment3,andscoreswereagainnormalizedfrom[‐6,88]to[0,1]foreaseof

analysis.Notethatbecausethenormalizationdidnotincludetheincreasedrangepossible

fromthetransferofprotection‐relatedfees,itwaspossiblefornormalizedscorestogo

beyond[0,1],butthisdidnotoccur.Unadjustedscorereferstovalueswhichdonotinclude

thesubtractionofprotectionorusefeespaidortheadditionofusefeesreceived,

correspondingtotheplainvalueofthesolutionaccordingtoitselements;adjustedscore

150

referstothesamevalueswiththeabovefeesaddedorsubtracted(whenpresent).All

analysesofscorewillrefertounadjustedscoreexceptwherenoted;ingeneraltherewere

nodifferencesbetweenresultsforadjustedandunadjustedscores.

7.3.Experiment4Results

7.3.1Overallmeans

MeandependentvariablesineachconditionareshowninTable7.2(seealsoFig.

7.1).Forgroupedparticipants,meanoverallandfinalscoresineachconditionwerenearly

identicaltoeachotherandtothoseobservedinthevisible‐scoresconditioninExperiment

3.Onaverage,minimumscoreswerelowerandmaximumscoreswerehigherinthe

protectionavailablecondition,butneitherdifferencewassignificant.Isolatedparticipants

achievedslightlyhighermeanoverallandfinalscoresthanthoseinExperiment3.

Figure7.1:Distributionofscoresforallpossibleteams.

151

Table7.2:Meanscore,guessdiversity,andchoicesourceproportionsbycondition

(PU:ProtectionUnavailable,PA:ProtectionAvailable)

Cond.OverallScore(Percentile)

FinalScore(Percentile)

GuessDiversity

Imitation Innovation Retention Retrieval

PU .451(93.3%) .525(97.5%) 60.1%* 6.9%* 14.6%* 75.6%* 2.2%

PA .446(92.6%) .530(97.5%) 65.9%* 6.2%* 17.8%* 72.9%* 2.3%

IsolatedPartic. .376(86.1%) .466(94.0%) ‐‐ ‐‐ 26.1% 61.0% 12.2%

*significantdifferencesbetweenconditions

7.3.2.Rounds

Linearmixed‐effectsmodelswereusedtoexaminetrendsacrossroundsforscore

andguessdiversity,witharandomeffectofparticipantgroup.Analysisofscoreversus

roundshowedverysimilarpositivetrendsforgroupedparticipantsineachcondition(PU:

F(1,712)=208.87,p<.0001,B=.627;PA:F(1,712)=283.72,p<.0001,B=.670).Isolated

participants’scoresincreasedsignificantlyacrossroundsaswell,butsignificantlylessso

thanforgroupedparticipants(F(1,657)=95.52,p<.0001,B=.498,meanincrease=0.150;see

Fig.5.4).Guessdiversityshowedcorrespondingdecreasesacrossroundsinboth

conditions(PU:F(1,712)=169.33,p<.0001,B=‐0.458;PA:F(1,712)=165.94,p<.0001,B=‐

.485;seeFig.7.2).

152

Figure7.2:Scoresincreasedandguessdiversitydecreasedataboutthesameratewhether

protectionwasavailableorunavailable.

Trendsforchoicesourcesacrossroundsshowedverysimilarpatternstothosein

Experiments2and3,withapproximatelythesamemagnitudeandsignificance:Imitation

andInnovationdecreasedsignificantlyoverrounds,andRetrievalandRetentionincreased

significantly.Therewasnosignificantdifferenceinslopeforanychoicesourcebetween

conditions,norasubstantialdifferenceincomparisontotheslopeoverroundsforeach

choicesourcefoundinExperiment3.Protectiondecreasedacrossrounds(F(1,712)=17.54,

p<.0001,B=‐0.170),whileuseofprotectedteamsincreased(F(1,712)=49.26,p<.0001,

B=0.331;seeFig.7.3).

153

Figure7.3:Protectiondecreasedacrossrounds,whileuseofprotectedteamsincreased.

7.3.3.Gameorder

Similarlinearmixed‐effectsmodelswereusedtoexaminetrendsacrossgameorder

foreachdependentvariablewithinconditions.Forthisanalysis,thegameordervaluefor

eachgamewascorrectedtoitsorderwithinthecondition,i.e.Game1or2ineach

condition.Scoreshowednosignificantchangeacrossgameorderineithercondition,and

guessdiversitydisplayedadecreaseacrossgameorderinbothconditions(PU:

F(1,30)=5.94,p=.021;PA:F(1,30)=4.76,p=.037;seeFig.7.5).Therewerenosignificant

changesacrossgameorderforanychoicesourceineithercondition(seeFig.7.5).

Withintheprotectionavailablecondition,protectiondecreasedacrossgameorder

(F(1,26)=9.79,p=.0043,B=‐0.217,meanchg.=‐0.020),butuseofprotected teamsdidnot

changesignificantly.

154

Figure7.4:Scoredidnotchangesignificantlyineithercondition,andguessdiversity

decreasedinbothconditions.

(a) (b)

Figure7.5:(a)ImitationandInnovationdidnotshowsignificantchangesacrossgame

orderineithercondition,nordid(b)RetentionorRetrieval.

155

Figure7.6:Protectiondecreasedsignificantlyacrossgameorder,whileuseofprotected

teamsshowednosignificantchange.

7.3.4.Groupsize

Trendsacrossparticipantgroupsizeforeachdependentvariablewithinconditions

wereexaminedusinglinearmixed‐effectsmodels,withtheparticipantgroupusedasa

randomeffectontheintercept.Slopesacrossgroupsizedidnotshowdifferencesbetween

conditionsforanydependentvariable,exceptwherenoted.Scoreincreasedsignificantly

withgroupsizeinbothconditions(PU:F(1,43)=27.19,p<.0001,B=0.512;PA:

F(1,43)=36.69,p<.0001,B=0.568;seeFig.7.7),andguessdiversityshoweda

correspondingdecreaseinbothconditions(PU:F(1,29)=28.96,p<.0001,B=‐0.661;PA:

F(1,29)=34.48,p<.0001,B=‐0.672;seeFig.7.7).Asforchoicesources,Imitationincreased

significantlyforlargergroupsinbothconditions(PU:F(1,29)=37.72,p<.0001,B=0.680;PA:

F(1,29)=37.20,p<.0001,B=0.699;seeFig.7.8a),whileInnovationdecreasedsignificantly

156

onlyintheprotectionavailablecondition(F(1,29)=8.94,p=.006,B=‐0.437;seeFig.7.8a).

NeitherRetentionnorRetrievalshowedsignificantchangesacrossgroupsize(seeFig.

7.8b).

Protectiondidnotshowasignificanttrendacrossgroupsize,whileuseofprotected

teamsincreasedinlargergroups(F(1,29)=37.45,p<.0001,B=0.751;seeFig.7.9).

Figure7.7:Asparticipantgroupsizeincreased,meanscoresinagroupincreased,andthe

diversityofofferedsolutionsdecreased.

157

(a) (b)

Figure7.8:Asparticipantgroupsizeincreased,(a)meanproportionsofImitationincreased

inbothconditionsandInnovationdecreasedonlyintheprotectionavailablecondition,and

(b)RetentionandRetrievalshowednosignificantchange.

Fig.7.9:Asparticipantgroupsizeincreased,protectiondidnotchangesignificantly,butuse

ofprotectedteamsincreased.

158

7.3.5.Differencesinimitation

Acrossbothconditions,approximately94.7%ofallguessesincludingImitation

wereofasingleparticipant.Atthetimeofsuchsingle‐sourceimitations,thescoreofthe

imitatedparticipantwasgreaterthanthatoftheimitatorinapproximately90%ofcasesin

bothconditions(seeFig.7.10a).Ofallinstancesofsingle‐participantimitation,the

probabilityofimitatingthetop‐scoringsolutioninthegroupwassignificantlyhigherinthe

protectionunavailableconditionthantheprotectionavailablecondition(t(34)=5.27,

p<.0001;seeFig.7.10b).Ananalysisoftheprobabilityofprotectionacrossscorerank

showedthatthebesttwosolutionspresentinanygivenroundwerenearlyalways

protected(seeFig.7.10c).

Toexamineseparatelyhowoftenandhowmuchparticipantsimitatedoneanother,

wemeasuredthemeanincidenceofguessesinwhichtherewasgreaterthanzeroImitation

(Imitationincidence),aswellasthemeanuseofImitationinthosecaseswhereitwas

greaterthanzero(Imitationproportion).MeanImitationincidencewassignificantlyhigher

intheprotectionunavailablecondition(0.205vs.0.162;F(1,92)=19.37,p<.0001),but

meanImitationproportionwaslower(0.341vs.0.390;F(1,89)=7.28,p=.008),andthe

distributionofmeanimitationproportionswasweightedslightlybutsignificantlymore

heavilytowardhighervaluesintheprotectionavailablecondition,asshownbya

Kolmogorov‐Smirnofftestofequalityofdistributions(D=0.1116,p<.0001;seeFig.7.11).

Inotherwords,participantsintheprotectionavailableconditioncopiedoneanotherless

frequentlybutinlargeramountsatatime.

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(a) (b)

(c)

Figure7.10:(a)Therewerestrongbiasestowardimitatingbetter‐scoringparticipantsthan

oneselfinbothconditions,and(b)asignificantlystrongerbiastowardimitatingthebest‐

scoringparticipantintheprotectionunavailableconditionthanintheprotectionavailable

condition;and(c)arelatedanalysisshowedthatthebesttwosolutionsinanygivenround

werehighlylikelytobeprotected.

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Figure7.11:ForguessesthatincludedatleastsomeImitation,participantsinthe

protectionavailableconditionhadhigherproportionsofImitationintheirguesses.

5.3.6.Choicesourcestrategy

AsinExperiment2,thechoicesourcesofeachnon‐isolatedparticipantoverthe

entiresessionwereanalyzed,andeachparticipant’schoicesourcestrategywascategorized

accordingtotheirproportionofeachsource.Participantswhosechoicescontainedone

sourceinanaverageproportiongreaterthantheglobalaverageforthatsourceplusone

standarddeviation,werelabeledwiththatstrategy.Forexample,aplayerwhoseguesses

overthecourseofasessionconsistedofagreaterproportionofImitatechoicesthanthe

averageforallotherparticipantsintheexperiment,plusonestandarddeviation,were

labeledashavinganoverallstrategyof“Imitate.”Thosewhofittheabovecriteriaformore

thanonechoicesource,ornone,werelabeledashavinga“Mixed”strategy.Thescore

distributionforeachstrategycategoryineachconditionisshowninFig.7.12.

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(a) (b)

Figure7.12:Scorevs.choicesourcestrategyin(a)protectionunavailableand(b)

protectionavailableconditions,showingthataconservativehigh‐Retentionstrategy

resultedinthebestperformanceinbothconditions,thoughhighlyImitativestrategiesalso

performedwell.

Alinearregressionofmeanindividualscorevs.meanindividualImitationguess

proportionshowedasignificantpositiverelationship(thatis,thegreateraparticipant’s

averageproportionofImitation,thebettertheparticipant’sscore)inbothconditions(PU:

F(1,142)=7.91,p=.006,B=0.230;PA:F(1,142)=3.96,p=.048,B=0.165;seeFig.7.13a).The

oppositewastrueforindividualscorevs.Innovation,whichdisplayedasignificant

negativerelationshipinbothconditions(PU:F(1,142)=120.30,p<.0001,B=‐0.677;PA:

F(1,142)=98.01,p<.0001,B=‐0.639;seeFig.7.13b).Apositiverelationshipheldfor

Retentioninbothconditions(PU:F(1,142)=56.24,p<.0001,B=0.533;PA:F(1,142)=53.38,

p<.0001,B=0.523;seeFig.7.13c).Finally,anegativerelationshipwasfoundforRetrievalin

162

bothconditions(PU:F(1,142)=4.88,p=.029,B=‐0.182;PA:F(1,142)=7.15,p=.008,B=‐

0.219;seeFig.7.13d).

AsinExperiment2,analysesofmeangroupscorevs.meangroupguessproportion

foreachchoicesourceshowedsimilarrelationshipsofthesamesignificanceanddirections

asthosenotedabove.Analysesofmeanindividualscorevs.meangroup(excludingthe

individual)guessproportionshowedsimilarrelationshipsaswell,withtheexceptionofthe

absenceofsignificantrelationshipsforRetentionorRetrieval.Plotsoftheseareomittedfor

clarity.Alltrendsnotedaboveweregenerallymonotonic;thatis,therewerenothresholds

orinflectionpointsbeyondwhichtherelationshipschanged.

Similaranalysesofprotectionshowednosignificantrelationshipwithscorefor

individuals(seeFig.7.14a),orattheothertwolevelsdiscussedabove(groupand

individualvs.groupothers),whilescorevs.useofprotectedteamsshowedasignificant

positiverelationshipforindividuals(F(1,142)=67.42,p<.0001,B=0.567;seeFig.7.14b),as

wellasforgroups(F(1,60)=72.99,p<.0001,B=0.740),andforindividualscoreversus

protectionbyothersinthegroup,excludingtheindividual(F(1,142)=40.86,p<.0001,

B=0.471).Allofthesamerelationshipswerefoundforbothadjustedandunadjustedscore.

Plotsoftheseareomittedforclarity.

163

(a) (b)

(c) (d)

Figure7.13:Higherindividualscoreswereassociatedwith(a)higherindividualImitation,

(b)lowerInnovation,(c)higherRetention,and(d)lowerRetrieval.

164

(a) (b)

Figure7.14:(a)Protectionshowednosignificantrelationshipwithscore,while(b)higher

useofprotectedteamswasassociatedwithhigherscores.

7.3.7.Improvements

Asinpreviousexperiments,improvementsweretalliedforeachparticipantineach

sessionandcondition.Histogramsofnormalizedimprovementshareinbothconditions

showedalessequitabledistributionofimprovementswithingroups(moreparticipants

withzeroimprovements,andfewerwithsharesnear1)relativetothescores‐visible

conditioninExperiment3(compareFigs.7.15and5.13).AKolmogorov‐Smirnofftestof

equalityofdistributionsindicatedthatthedistributionsineachconditionwerenot

significantlydifferent.However,theuppertailofthedistributionwasessentiallyshifted

upwards(i.e.thehighestimprovementsharesinthePUconditionwerereplacedbyeven

highersharesinthePAcondition),thoughthehighestachieversineachconditionwere

entirelydifferentsetsofindividuals.Meanoverallscorealsoshowedastrongpositive

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correlationwithimprovementshareinthePAcondition(F(1,112)=49.98,p<.0001,

B=0.348),butthisrelationshipwasnotevidentinthePUcondition.

Themeanchoicesourceproportionsforguessesthatresultedinscore

improvementsandthosethatdidnotareshowninTable7.3.Intheprotectionunavailable

condition,guessesthatyieldedimprovementshadhigherInnovation(t(417)=‐9.78,

p<.0001)andlowerRetention(t(395)=6.01,p<.0001)relativetonon‐improvements.Inthe

protectionavailablecondition,therewashigherImitation(t(549)=‐2.78,p=.006),lower

Innovation(t(574)=2.86,p=.004),andlowerRetrieval(t(682)=3.37,p=.0008)for

improvementsthannon‐improvements.Ofallimprovements,aboutthesameproportionin

eachconditionresultedfromguessesthatincludedImitation(PU:.252vs.PA:.224).

In51.2%ofimprovementsintheprotectionunavailableconditionand43.9%inthe

protectionavailablecondition,thefocalplayerimitatedatleastonepeerwhohad

previouslyimitatedthefocalplayer.Inotherwords,aplayerwhowasimitatedbyanother

playeroftenlaterimitatedthatsameplayerinthecourseofcreatinganimprovement,and

thishappenedmoreoftenwhenprotectionwasunavailable.

166

Figure7.15:Histogramsshowingdistributionsofimprovementswithingroupsineach

condition.

Table7.3:Meanchoicesourceproportionsforimprovementandnon‐improvement

guessesineachcondition.

Condition Improvement %ofguesses Imitation Innovation Retention RetrievalNo 94.7% 7.9% 13.6%* 75.7%* 2.0%PU Yes 5.3% 9.1% 20.1%* 69.0%* 1.7%No 92.5% 7.0%* 16.8%* 73.0% 2.3%PA Yes 7.5% 10.0%* 14.4%* 73.9% 1.3%

*significantdifferencesbetweenimprovementsandnon­improvementswithin

condition

7.3.8.Guesssimilarity

Acomparisonbetweenthemeansimilarityofparticipants’mostrecentguessesto

thosewhomtheyimitated,andtothosewhomtheydidnotimitate,revealedslightbut

significantdifferencesinbothconditions.Intheprotectionunavailablecondition,there

167

weresimilarityvaluesof.576forimitatedvs..545fornon‐imitatedguesses(t(2511)=‐2.90,

p=.0037;seeFig.7.16a).Inthescores‐invisiblecondition,thereweresimilarityvaluesof

.491forimitatedvs..457fornon‐imitatedguesses(t(2051)=‐3.18,p=.0014;seeFig.7.16b).

Inotherwords,priortoimitation,theaverageimitators’guesswasmoresimilartothatof

theimitatedparticipant(s)thantothoseofothersintheprotectionunavailablecondition,

andthisrelationwasfoundbutwasslightlylessprominentintheprotectionavailable

condition.

(a) (b)

Figure7.16:(a)Intheprotectionunavailablecondition,imitators’previousguesses

showedgreatersimilaritytotheguessestheyimitatedthantothosetheydidnotimitate,

while(b)inthescores‐invisiblecondition,asimilarbutweakereffectwasobserved.

7.3.9Frequencyandmomentumbias

AsinExperiment1,wemeasuredthebiasofparticipantstochooseanicon

accordingtoitsfrequencyinpeers’choices.Toreiteratebriefly,wemeasuredthemean

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probabilityofImitationandInnovationforanyiconnotalreadyincludedonaplayer’s

team,basedonthefrequencyofitsappearanceonpeers’teamsintheplayer’sdisplay,and

comparedthemtoexpectedchancebaselines.

Linearmixed‐effectsanalysisofimitationprobabilityversuschoicefrequency

showedapositivefrequency‐dependentImitationbiasthatwassignificantlygreaterthan

chanceintheprotectionunavailablecondition(F(1,258)=355.39,p<.0001,B=.722),but

significantlylowerthanchanceintheprotectionavailablecondition(F(1,258)=387.81,

p<.0001,B=.714;seeFig.7.17a);bothbecameapparentathighervaluesofchoice

frequencythaninExperiment3.Thereweresimilarpositivefrequency‐dependent

Innovationbiasesabovechanceinbothconditions(PU:F(1,258)=133.15,p<.0001,B=.517;

PA:F(1,258)=192.79,p<.0001,B=.601;seeFig.7.17b).

Wealsorepeatedtheanalysisof“choicemomentum,”bytallyingthechangeinthe

numberofplayerswhoseteamsincludedtheiconintheprevioustworounds,aswellas

thenumberoftheremainingplayerswhoaddedittotheirteaminthecurrentroundvia

ImitationorInnovation,andnormalizingforgroupsize.Afterlog‐transformingthe

Imitationprobabilitydatatoachieveanormaldistribution,t‐testsofImitationprobability

fornegativeandpositivechangesinchoicefrequencyshowedsimilarsignificantpositive

momentumbiasesinbothconditions(PU:t(304)=‐8.66,p<.0001;PA:t(299)=7.76,

p<.0001;seeFig.7.18a).SlightpositivemomentumbiaseswerealsofoundforInnovation

inbothconditions(PU:t(385)=‐3.40,p=.0007;PA:t(346)=‐5.54,p<.0001;seeFig.7.18b).

169

(a) (b)

Figure7.17:(a)Therewerebiasestowardchoosingelementsthatweremorefrequently

representedonotherteamsintheprotectionunavailablecondition,andlessfrequently

representedonotherteamsintheprotectionavailableconditionforImitationand(b)

biasestowardmorefrequentelementsforInnovationdecisionsinbothconditions.

(a) (b)

Figure7.18:Therewerebiasestowardchoosingelementswhoserepresentationonother

teamswasincreasinginbothconditionsfor(a)Imitationand(b)Innovationdecisions.

170

7.3.10.Surveyresponses

Thesurveydistributedtoparticipantsaftertheendofthelastgameineachsession

isincludedinappendix7.A.Thefirsteightquestionsonthesurveyweremultiple‐choice,

withpossibleresponsesona7‐choiceLikertscale,coded1‐7.Questions2,3,and4were

relatedtoprotectionandhadanadditionaloptionfor“doesnotapply,”whichwascodedas

0.Thelasttwoquestionswerefree‐response;oneaskedparticipantstodescribetheir

strategies,andmostresponsesweresomevariationona“copy‐if‐betterandthenmake

smallchanges”strategy;theotheraskedforanyfurthercomments,andmostresponses

wereeitherblank,orshort(generallypositive)commentslike“fun”orinteresting.”For

quickreference,theeightmultiple‐choicequestionsareshowninTable7.4.Stripchartsof

responseswithkerneldensityestimatesareshowninFig.7.19.

Table7.4:Multiple‐choicesurveyquestions,withresponsesassociatedwiththeextreme

lowandhighendsofthescale.Thosesignificantlyassociatedwithhigherindividualscores

areshowninbold.

increaseyourownscore(withoutregardtothescoresotherplayersmighthave)Q1 Duringthegame,didyoumostlytryto…?

scorehigherthanotherplayers

keepothersfromusingyoursolutionsQ2 If/whenyouprotectedyoursolutions,wasitmostlyto…?

getpaymentforothers'useofyoursolutions

copythewholeteamandpaythefeeQ3 Whenyouwantedtouseanotherplayer’sprotectedteam,didyougenerallypreferto…?

copyitandthenchangeittoavoidpaying

NeverQ4

Whenyoufoundateamwitharelativelyhighscore,didyoueverintentionallyleaveitunprotectedsothatotherscouldcopyitforfree? Everytime

171

VeryeasyQ5 Howdidyoufeelaboutthedifficultyofthetask?Veryhard

otherplayers’teamsQ6 Didyouchoosecreaturesmoreoftenfrom…?theleague

otherplayers’teamsQ7 Didyoufindthatyourscoreswerebetterwhenyouchosecreaturesfrom…?

theleague

LuckQ8 Doyoufeelthatsuccessinthistaskwasbasedmoreon…?

Skill

(a)

172

(b)

(c)

Figure7.19:Responsestothemultiple‐choicesurveyquestionsinTable7.4,plottedas

stripchartswithkerneldensityestimatesandmeanlines,separatedasfollowsforclarity:

responsesfromgroupedparticipantsto(a)non‐protection‐relatedquestionsand(b)

protection‐relatedquestions,and(c)responsesfromisolatedparticipantstoQ5andQ8.

173

Relationshipsbetweenplayerscoresandresponsestoeachquestionwereanalyzed

usingamixed‐effectslinearmodelwithparticipantgroupasarandomeffect.Higherscores

wereassociatedwithresponsesattheupperendofQ1(scorebetterthanothers)

(F(1,256)=22.68,p<.0001,B=0.236),theupperendofQ2(getpaymentfromothers)

(F(1,252)=6.39,p=.0122,B=0.140),thelowerendofQ3(copythewholeteamandpay)

(F(1,243)=14.91,p=.0001,B=‐0.210),thelowerendofQ4(neverleaveunprotected)

(F(1,242)=6.73,p=.0100,B=‐0.142),thelowerendofQ6(choosefromothers’teams)

(F(1,254)=19.88,p<.0001,B=‐0.225),andtheupperendofQ8(performancebasedonskill)

(F(1,254)=8.15,p=.0047,B=0.148).Inexaminationsofresponsetrendsacrossparticipant

groupsize,wefoundjustonesignificanttrend:responsestoQ2weresignificantlyhigher

(getpaymentfromothers)inlargergroups(F(1,29)=8.88,p=.0058,B=0.243).

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7.4.Experiment4Discussion

7.4.1.SimilaritieswithExperiment3

Aspredicted,resultsintheprotectionunavailableconditionofExperiment4(E4PU)

weregenerallysimilartothoseinthevisible‐scoresconditionofExperiment3(E3SV).

PerformancewasslightlybetterinE4PUthanE3SVaspredicted,whichmayhavebeendue

totheincentiveofcashpayment,ortheextratimetomakedecisionsabouteachround's

candidatesolution,thoughunfortunatelywecannotdifferentiatebetweenthesetwo

factorsascauses.IsolatedparticipantsinE4alsodidbetterthanthoseinE3,which

reinforcesthisexplanation.ImitationwasmarkedlylowerandInnovationhigherinE4PU

thaninE3SV,whichmayhavebeenacarryovereffectfromthePAcondition,inwhichthese

differenceswereevenmoreextreme.TrendsofRetentionandRetrievalovergroupsize

thatwerepresentinE3SVwerenotpresentinE4PU,andtherewasanegativecorrelation

ofscorewithRetrievalinE4PUthatwasnotpresentinE3SV,butineachcasethemissing

relationshipwasnominallypresentintheotherexperiment,butnotsignificant.Theless

equitabledistributionofimprovementshareinE4PUrelativetoE3SVcouldbeattributed

toadifferentialcrowding‐out(FreyandJegen,2001)ofintrinsicmotivationtoachieve

improvementsforsomeparticipantsandnotothersbythecashpaymentofferedinE4.

7.4.2.Performance

PredictionsconcerningthePAconditionweregenerallyborneoutaswell.

Maximumscoreswereslightlyhigher,butoverallscoreswereactuallyslightlylowerinthe

PAcondition,thoughneitherdifferencewassignificant.This,alongwiththeincreased

Innovation,decreasedImitation,andincreasedguessdiversityrelativetoPU,accordswith

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thepredictionsmadeforthiscondition:thegreaterincentivesforexplorationledto

increasesinInnovationandlessconvergence,andsomegoodreturnsintheformofslightly

moreimprovements.However,thegreatergeneralriskofexploration,aswellasless

efficientpropagationofbetterperformingsolutionsthroughImitation(becausethebest

solutionsweregenerallyprotected)ledtoawashingoutofthebenefitsofimprovements

bylowerscoresencounteredalongtheway,ratherthanfurtherimprovementofthebetter

solutionsthatwerefound.

7.4.3.Strategy

Aspredicted,theavailabilityofteamprotectionalsoaffectedtheuseofotherkinds

ofinformationinimitationstrategies:PAparticipantsshowedweakersimilaritybias,anda

reversaloffrequencybias,atleastforImitation.Theformercouldhavebeenduetoan

inclinationtowardsaltationiststrategiesasseeninE3SI,whilethelattercouldhavebeen

duetohigher‐frequencyiconstypicallybeingonprotectedteams.Thedecreasein

ImitationincidenceandincreaseinImitationproportionwhenprotectionwasavailable

indicatesthatthefeeforimitationwasadisincentiveforImitation,butwhenImitationwas

pursued,participantseitherkepttheimitatedguessunchanged(totakeadvantageofthe

presumedimprovementinscoreand“gettheirmoney’sworth”fortheusefee),orchanged

relativelyless(inorderto“inventaround”theprotectedsolutionwithoutasmuchriskof

loweringthescore).

Theassociationofhigherscoreswithhigheruseofprotectedteamswaslikelydue

tothefactthattheusefeewasquitesmallrelativetothepotentialbenefitinmostcases.

Thelackofarelationshipbetweenprotectionandscorecouldhavebeenduetogeneral

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overuseofprotection;thetypicalresponsetoQ4onthesurveyindicatesthatformost

participantsthedefaultactionupondiscoveringahigh‐scoringsolutionwastoprotectit,

andthisisborneoutinFigure7.10c.InthePAcondition,theincreaseduseofImitationin

improvementsrelativetonon‐improvementsshowsthatforthosewhorecognizedthe

valueofusingprotectedteams,Imitationwasquiteaproductivestrategy.

Thedecreaseinprotectionandincreaseinuseofprotectedteamsoverroundscan

bothbeexplainedbythefactthatimprovementsavailablefordiscoverybecame

increasinglyrareasparticipantsdiscoveredbettersolutionsandmovedhigherinthescore

distribution.Protectiondecreasedbecausefewerandfewerguessesyieldedprotection‐

worthy,relativelyhigherscores,andtheuseofprotectedteamsincreasedbecausethe

dwindlingsupplyofscore‐improvingsolutionsstokedthedemandforusingthoseofothers

andmadeparticipantsmorewillingtopaytherelatedfee.Theincreaseinuseofprotected

teamsacrossparticipantgroupsizecanbeconsideredanextensionofthegenerallygreater

Imitationinlargergroups.

Thoughtherewasnosignificantchangeinscoreorchoicesourcesacrossgame

orderwithinconditions,thedecreaseinthenumberofgamesperconditionrelativeto

previousexperimentsmadeforlessdatainwhichtodetecttrendsofthissort.The

decreaseinprotectionovergameorderwaslikelyanadaptationtothefailureofthe

always‐protectstrategy(displayedinQ4responsesandthenear‐universalprotectionof

thebest‐scoringsolutions)toturnaconsistentprofit(asshownintheflatscoreversus

protectionresults).

7.4.4Self‐reportedmotivationsandmethods

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Despitereceivinginstructionsthatthegoalofthetaskwasmerelytomaximizeone’s

owntotalscoreoverthecourseofeachgame,aswellasbeinginformedthatpaymentwas

contingentonlyonindividualperformance,responsestoQ1revealedthatmany

participantswerejustasmotivated(ormore)toincreasetheirperformancerelativeto

others.Thosewhoreportedsuchrelativeperformancemotivationalsotendedtoscore

higherthanothers,asdidthosewhosawperformanceinthegameasamatterofskill

ratherthanluckinQ8(thoughmostparticipantsbelieveditwasthelatter).Q2showedthat

participantsweresomewhatevenlydividedbetweenprotectingtokeepothersfromusing

theirsolutionsandgettingpaymentforthem,andresponsestoQ3showedthat

participantswerealsofairlyevenlydividedbetween“licensing”and“inventingaround”

others’protectedteams.

7.5.Conclusions

7.5.1.Similaritiesanddifferenceswithpreviousresults

Inthisexperiment,wefoundpatternsofresultsverysimilartothoseinprevious

experiments,buttherewerealsosomecuriousnewcombinationsoftheseeffects.

Specifically,weobservedinbothconditionstheby‐nowfamiliarresultthataconservative

approachtothistaskpaidoff:relativelyhighusageofImitationandRetentionwere

associatedwithhighscores,andInnovationandRetrievalwithlowscores;trends

displayingtheserelationshipsdifferedverylittleacrossconditions.

Besidestheresemblancebetweentheprotectionunavailableconditionof

Experiment4(E4PU)andExperiment3(E3SV)notedearlier,theprotectionavailable

condition(E4PA)showedsomeresultsthatresembledthoseoftheinvisible‐scores

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conditioninExperiment3(E3SI)aswell.Forinstance,therewasareducedtendencyto

imitatetop‐scoringsolutionsinE3SIwasduetotheimpossibilityofdistinguishingthe

qualityofsolutions,andinE4PAduetothedisincentiveofpayingtheusefeefortop‐

scoringsolutions(whichweregenerallyprotected).Therewasalsoincreaseddiversityand

innovationrelativetothealternateconditionforboth,andadecreaseintheuseof

similarity‐andfrequency‐biasedimitation.However,thesechangesledtothediscoveryof

fewerimprovementsinE3SIrelativetoE3SV,whilethereweremorefoundinE4PA

relativetoE4PU,thoughthisdidnotleadtogreateroverallorfinalscores.Overall,it

appearsthattheextraincentiveforInnovationinE4PAledtosomeimprovementswhose

benefitswerecanceledoutbytheworsesolutionsencounteredintheexplorationprocess,

andtherewasdisincentiveforimitationwhichresultedinfewersequentialimprovements,

whichmayhaveimprovedaverageperformancewithlessrisk.

7.5.2.Similaritiesanddifferencesbetweenexperimentalandreal‐worldpatentsystems

Thisexperimentfeaturedapatent‐likesystemforgoverningtheuseofinnovations,

butwasinnowaymeanttoaccuratelyrepresentthecomplexitiesofarealpatentsystem.

Majordifferencesbetweenthistaskandsuchrealsystemsinclude:ourautomatic

“licensing”ofpatentedinnovations,withnoabilityforpatenteestorefusetogranta

license,negotiatethelicensingfee,orinfringeothers’patentswithoutlicensing;

unambiguouspatentscopeandnoabilitytovaryordisputethebreadthofpatented

features;nodistinctionbetweendiscoveryandproductionofinnovations;noabilityto

“opensource”innovationssuchthattheycouldbeusedfreelybyothersbutnotpatented;

andnoabilitytosellorotherwisetransferpatentrightsbetweenparticipants.Wefeltthat

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testingtheeffectofachangeinincentivestoinnovateinamoregeneralsearchdomain,and

establishingcontinuitywithourpreviousexperimentsinthisdomainweremoreimportant

thanattemptingtoreplicatemorefeaturesofpatentsystems.However,anexperimentthat

didincludeallofthefeaturesnotedaboveactuallyfoundthatacompletelycommons‐based

(patent‐free)systemoutperformedbothapatent‐onlysystemandamixedpatent‐

commonssystem(Torrance&Tomlinson,2009).

Besidesthedistinctionbetweendiscoveryandproductionofinnovationsinthereal

world,thereisalsothefactthatphysicallyproducingmanyinnovativeproductsdepends

onrivalrousrawmaterialresources.Again,therewasnoprovisionforthisfactinour

experiment,butitwasincorporatedinanotherstudytocreateamarket‐basedmechanism

forpromotinginnovation(Meloso,Copic,&Bossaerts,2009).Similartoourexperiment,

participantsinthisstudyexploredvaryingcombinationsofoptionstosolveaproblem;the

primarydifferencewasthatinthe“patent”condition,amonetaryprizewasgiventothe

firsttodiscovertheoptimalsolution,andinthe“market”condition,participantsbought

andsoldsharesineachoption,andsharesofoptionscontainedintheoptimalsolutionpaid

amonetarydividendattheendofthegame.Melosoetal.(2009)foundnobenefitforthe

patent‐basedsystemoverthemarket‐basedsystem:theoptimalsolutionwasfoundinan

equalnumberofrunsofeachcondition.However,theoptimalsolutionwasfoundbya

greaterproportionofparticipantsinthe“market”condition.Theincentiveofprofiting

fromthesalesofsharesintheoptimalsolutionmotivatedmoreparticipantstofindthe

optimalsolutionthanaprizethatonlyoneofthemcouldwin.Thesharepriceofeach

optioninMelosoetal.’sstudyalsosignaledparticipantsaboutthegroup’scollectivebelief

initsvalue,whichsupportedalearningstrategysimilartothefrequencybiasseeninour

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results,andthe“filtering”ofoptionsusedinthesociallearningstrategiestournamentof

Rendelletal.(2010).

7.5.3.Polycentricinnovation

Thereremainlargedifferencesbetweentheaboveexperimentaltreatmentsand

manyreal‐worldintellectualdiscoverycontexts,mostobviouslyinthescaleofdiscoveries,

andtheinvestmentsoftimeandotherresourcesrequired.Butthefactthatmany

predictionsfromthetraditional“reward”and“prospect”theoriesofpatentshavebeen

contradictedorremainunconfirmedintheaboveexperimentalresults,aswellascross‐

nationaleconometricstudies(Park&Ginarte,1997),large‐scalereviewsofdatarelatedto

patentingbehaviorandchangesinpatentlaw(Bessen&Meurer,2008;Boldrin&Levine,

2008),andavarietyofothermeasures(seeChapter6)shouldgiveuspauseincontinuing

toendorsesuchtheories.Theincreasinglywell‐studiedperformanceofalternatemodelsof

innovationbyindividualusersandgroupsengagedinopencollaboration(Baldwin&von

Hippel,2009;Strandburg,2009;Benkler,2006)showusthattherearemanypossibilities

formoreequitable,efficient,andsustainablewaysofcreatingbeneficialinnovationsand

supportingaknowledgecommons.

MazzoleniandNelson(1998)notethatthetheoriesusedtojustifyIP(thoseof

incentivesforcreation,disclosure,commercialization,andefficientexplorationof

innovations)arenotuniversallyapplicableandinsomecircumstancesconflictwitheach

other.Theyalsonotethatthesetheoriesmakeassumptions(implicitlyorexplicitly)about

severalimportantfeaturesofcontextsinwhichinnovationoccurs:(1)“Thenatureand

effectivenessofmeansotherthanpatentstoinduceinventionandrelatedactivities”(a

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generaleffectivenessquestion)(2)“Whetherthegroupofpotentialinventorsislikelyto

workondiverseandnon‐competingideas,orwhetherthegroupislikelytobefocusedona

singlealternativeorasetofcloselyconnectedones.”(i.e.thestructureofthesearchspace)

(3)“Thedeterrenteffectofthepresenceofpatentsonunauthorizeduseofatechnology

andonthetransactioncostsinvolvedinlicensinganinvention.”(issuesrelatedto

competingfollow‐oninnovationsandanticommonsconcerns)(4)“Whetherthemultiple

stepsintheinvention,development,andcommercializationofanewtechnologytendto

proceedefficientlywithinasingleorganization,orwhetherefficiencyisenhancedif

differentorganizationsareinvolvedatdifferentstagesoftheprocess.”(issuesrelatedto

competitionandcentralization)(5)The“topographyoftechnologicaladvance,”i.e.“the

mannerinwhichinventionsarelinkedtoeachothertemporally,andassystemsinuse”

(alsodealingwithsequentialinnovationsandthestructureoftheproblemspace)

(Mazzoleni&Nelson,1998,p.1033).

Variationsintheseconditionsacrossdifferentinnovationcontextspromptachange

fromasking“Whichtheoryiscorrect?”to“Wheredoeseachtheoryapply?”Itiseasytosee

wherealternatemodessuchasuserinnovationoropencollaborationcouldgainpurchase

underthisframework,bymakingchangestotheassumptionsembodiedintraditionalIP

theories.Ratherthancentralizinginnovationdecisionsinpatent‐holdingindividualsor

firms,thesealternatemodesincreasetheflexibilityofthegovernanceofprovisionand

appropriationinaknowledgecommons,andsubjectthemtonormsdeterminedbythe

relevantcommunitiesofusersandinnovators.Asseenintheanalysesofpatent

performanceandvalueacrossindustries(Bessen&Meurer,2008),conditionsaround

inventionprocessesindifferentfields(e.g.pharmaceuticalsversussoftware)couldsupport

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avarietyofdifferentpracticesandorganizationalstructuresaroundthediscoveryanduse

ofinnovations,withdifferentrulesgoverningactionssuchascoordinationanddisclosure

ofcontributionstothecommons.Someofthesepracticesarealreadyinuseinsituations

suchasanonprofitpatentpoolforAIDStreatmentsindevelopingcountries(UNITAID,

2010),androyalty‐freelicenserequirementsforworldwidewebtechnologystandards

(WorldWideWebConsortium,2004).Atthesametime,thereisaplaceforhigherlevelsof

organizationandgovernance.Asmentionedearlier,IPrightscanbeusedtoresolveorpre‐

emptlegaldisputesbetweenknowledgeusersorusercommunities(O’Mahony,2003).It

hasalsorecentlybeenarguedthattheWorldIntellectualPropertyOrganization

(historicallyacoalitionforthepromotionofIPrightsandenforcement)shouldbere‐tooled

asamoregeneralinternationaladministrativeforumforconsideringandimplementing

policiesrelatedtoevolvingmodesofinnovation(Strandburg,2009).Thisrelianceonmix

ofvariousformsandscalesofauthoritywithoverlappingjurisdictions(asopposedto

completelycentralizedordecentralizedauthority)hasbeenfoundtobeanimportant

factorinthegovernanceofpublicgoodsandcommon‐poolresources,inwhichithas

becomeknownas“polycentric”governance(Ostrom,Tiebout,&Warren,1961;Andersson

&Ostrom,2008;Ostrom,2008).

Thereareundoubtedlysomeinnovationsthatmayhavebeendelayedornotcreated

atallapartfromsomeformofpatentsystem,buttherearealsoinnovationsthatwere

mademostlywithoutit(suchasmanyopen‐sourcesoftwareprojectsandmuchacademic

research)whichwouldprobablynothavebeencreatedifeachcomponentwassubjectto

patentprotection.Ratherthanarguingfortheabolishmentofthepatentsystem,these

innovationsdemonstratethatapolycentricsystemofknowledgecommonsgovernanceis

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possible,desirable,andinfactisalreadyuponus.Studiessuchasthosedescribedinthis

dissertationcanaidinunderstandingthecauses,consequences,anddynamicsofdiscovery

undervariousformsofgovernance,andthereforeinimprovingthepracticalprocessesof

discoveryforthebenefitofall.

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7.A.ProtectionchoicewordinginExperiment4

Protectionchoicedialog:attheendofeachroundexceptthelast,participantsinthe

protectionavailableconditionwhoseteamwasnotalreadyprotectedbyanother

participantwereshownadialogboxwiththefollowingtext(inquotes)andbuttons(in

brackets):

“Doyouwanttoprotectyourteam?Thiswillcostyou4points.”

[ProtectMyTeam] [Don’tProtectMyTeam]

Protectionconfirmation:Iftheparticipantclickedthe[ProtectMyTeam]button,a

dialogboxwasdisplayedwiththefollowingtextuntilthenextroundbegan:

“Yourteamwilbeprotectedfor3rounds.Youhavebeencharged4points.”

Protectiondenied:Iftheparticipantclickedthe[ProtectMyTeam]buttonand

anotherparticipanthadprotectedthesameteamfirstduringthesamepost‐roundchoice

period,adialogboxwasdisplayedwiththefollowingtextuntilthenextroundbegan:

“Sorry,someoneelseprotectedthisteambeforeyou.”

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Protectiondeclineconfirmation:Iftheparticipantclickedthe[Don’tProtectMy

Team]button,adialogboxwasdisplayedwiththefollowingtextuntilthenextround

began:

“Youchosenottoprotectyourteam.”

Previousprotection:Ifadifferentplayerhadprotectedthesameteamorateam

withinoneicondifferenceinapreviousround,thefollowingmessagewasdisplayed

insteadoftheProtectionchoicedialog:

“Yourteamthisroundcannotbeprotected.Waitingforotherstoprotecttheir

teams…”

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7.B.Post‐tasksurveyinExperiment4

Thefollowingsurveywasdistributedtoparticipantsfollowingtheendofthelast

gameineachsession.

Front

187

Back

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8.GeneralDiscussion

8.1.Conclusionsandcontinuations

Whenoneobservesothersforcluesaboutbeneficialbehaviors,itisimportanttobe

attentivetothemanypossibledifferencesbetweenthecontextstheyencounterandthe

relatedsituationsinwhichoneexpectstofindoneself.Thesecanbeduetochangesinan

environmentovertime,ordifferenceswithinandbetweenenvironmentsduetothingslike

climate,culture,orthecapabilitiesbroughttothepresentfrompreviousexperience.

Similarly,theexperimentalresultswehavesharedinthisdissertationaresubjectto

caveatsaboutthecontextinwhichweobtainedthem,butwebelievetheyoffersome

insightintocommonconflictsandmeritsubstantialfurtherstudy.

Thegoaloftheseexperimentswastoexaminehowgroupsofpeoplefindsolutions

toproblems,byadaptingtheirbehaviortotheirenvironmentsandtoeachotherovertime,

undervaryingcombinationsofinformationandincentives.Situationsthatfitthis

descriptionareubiquitiousinthelivesofhumansandothersocialanimals,butnotyetwell

understood.Theyarefullofcomplicatingandconfoundingfactorsthatmakeitdifficultto

findtheimportantfactorsthatcausetheoutcomeswesee.Intheseexperiments,wepared

awaymanyofthecomplexitiesofreal‐worldsociallearningtoenablerelativelysimple

interactionsinacontrolledproblemenvironment,sothatwecouldobserveparticipants'

behaviorunencumberedbyatleastsomeofthesecomplicatingfactors.Forinstance,we

didnotallowparticipantstospendpointsonimaginarylawyerswithwhichtosueeach

otherforvirtualpatentinfringement(Torrance&Tomlinson,2009),nordidwebuildan

artificialforagingapparatusforthemtopeckat.Wehopedtofindcommonalitiesbetween

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aspectsofdifferentkindsofexploration,suchasbirdssearchingforfoodandpeople

searchingforgoodideas,byabstractingfrommanyoftheirspecifics.

Thisquestforanidealabstractioncancreatetwokindsofflaws:first,itcanleave

outimportantqualitiesoftheeventsweareattemptingtomodel;second,thespecific

detailsthatarechosentoimplementthegeneralqualitieswewishtostudywillby

necessityintroducedistortionsoftheirown.Toconcludethisdissertation,wewilldiscuss

someoftherelevantaspectsofreal‐worldsociallearningandexplorationthatourtasks

didnottakeintoaccount,aswellassomeoftheartificialcharacteristicsthatmayhave

distortedparticipants'behavior,beforesummarizingthefindingsthatwebelievehave

validitybeyondourspecificparadigmsandshouldbeexaminedfurther.

8.2.Omissionsandcommissions

Weattemptedtoprovideappealing,understandable,andfairlyneutralproblemsfor

participantstosolve,whichdidnotundulyfavorcertaincognitiveassets(e.g.verbalor

mathematicalknowledge)thatcouldhaveintroduceddifferencesinbehaviorunrelatedto

ourdesiredphenomena.Inrealsearchsituations,ofcourse,historyandpreparationmatter

‐‐peoplebringallsortsofpreviousknowledgeandexperiencetobearonnovelsituations,

andtheseaffectoutcomesenormously.Thereisnosuchthingasa"pure"searchtask,

unmooredfromanyspecificskills.Traitsthatarepresumablyimportanttoperformancein

ourtaskssuchaslargeworkingmemoryandstrategicthinkingarebynomeansevenly

distributedamongthepopulation,norisenthusiasmforpuzzles,virtualpets,orfantasy

sportsleagues,elementsofwhichwetriedtoincorporateinordertomakethetask

interesting.

190

Inaddition,muchoftheknowledgeandexperiencethatpeoplebringtonewtasks

concernstheirfellowproblemsolvers,particularlytrustandotherbeliefsaboutothers'

capabilitiesandintentions.Peoplearepoliticalanimalsaswellassocialanimals,andthese

beliefs,andhowtheyarecreated,maintained,andmanipulated,areabsolutelycentralto

sustainedinteractionsingroups.Usingparticipantswho(presumably)knewlittleabout

eachotherbeforehandreducedthepossibilityoftheseimportantphenomenahaving

effectsonthecoordinationofbehavior.Thedevelopmentanduseofsuchinterpersonal

knowledgewasalsopreventedbylimitingparticipants'interactionsstrictlytothepassive

sharingofinformationabouttheirsolutions;theywerenotpermittedothermethodsof

communicationwitheachother(suchasachatinterface),ormanipulationofthe

environment(suchastaggingoficons).Wealsoomittedexplicitidentifyinginformation

aboutpeers,andpreventedimplicitidentificationbyavoidingconsistentpositioningof

eachparticipant'schoicesinthetaskdisplays.Capabilitiessuchasstableevaluationof

groupmembers'behavior,discussionandcollectivedeterminationofnormsare

particularlyknowntoaffectoutcomesinpublicgoodandcommon‐poolresourcedilemmas

(Ostrom,Gardner,&Walker,1994).Relatedly,eachgameinourtasklastedonlyafew

minutes,andthewholesessionwaslessthananhour;inreality,thelong‐term

sustainabilityofanysystem,letalonesomethingascomplexasaknowledgecommons,

cannotbeestimatedinsuchashorttime.

BeyondthespecificdetailsofpatentsystemsthatwementionedomittinginChapter

7,theeconomicvalidityofourtaskislimitedbythefactthattherewasnocostfor

explorationbeyondtheopportunitycostofforegoingotheroptions.Manyrealexploration

tasks(e.g.pharmaceuticaltrials,mineralexploration,orsoftwaredebugging)involve

191

substantialinvestmentsoftimeandotherresourcesbothupfrontandonacontinuing

basis.Therelativelyshortlengthandnarrowbreadthofprotection,amountsforprotection

andusefees,andtheoveralllevelofmonetarypaymentcouldraisesimilarobjections.

Becauseoftheabovedifferences,wemustbecautiousaboutgeneralizingour

resultstoobroadly,andourconclusionsmustbetestedinothersociallearningand

explorationparadigmstoobservetheeffectsoftheseandothercontextualfactors.

8.3.Summaryoffindings

Despitetheseconcerns,webelievethat(a)ourresultsmakeasubstantial

contributiontoknowledgeaboutthecauses,consequences,anddynamicsofsociallearning

andsearch;(b)thattheyhavesubstantialvaliditybeyondthetaskandparticipantsthat

generatedthem;and(c)thattheycanleadtofurtherfertileinvestigationinthelaboratory

andthefield.

Wefoundthatourhumanparticipantsusedseveralsociallearningstrategies

previouslystudiedinotherspecies(Laland,2004),suchascopyingbetter‐performing

peers,copyingsolutionelementsthataremorefrequentamongpeers,andcopyingwhen

uncertainaboutthereturnstoasociallearning.Wealsofoundevidenceforcopying

solutionssimilartoone'sown,whichhasbeenexaminedinstudiesofinnovationdiffusion

asbackwardscompatibility(Rogers,2003),aswellascopyingsolutionelementsthatare

increasingratherthandecreasinginfrequencyamongpeers,asobservedinarecentstudy

ofbaby‐namingdata(Gureckis&Goldstone,2009).Wealsofoundthat,ratherthansimply

fallingbackonalternatesociallearningstrategies(suchasfrequencybias)when

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performance‐basedimitationwasunavailable,theuseofeachsourceofinformationwas

usedindifferentwaysaccordingtothespecificincentivesandrisksinvolved.

Participantsusedfairlyconservative,incrementaliststrategiestoexplorecomplex

problemspaces,sothatinitialsatisfactorysolutionscouldbeusedasabasisforfurther

developmentviasmallamountsofbothimitationandinnovation.Thesetacticsallowed

participantstoprogressivelyandcollectivelynarrowtheirsearchtowardbetterregionsof

theproblemspacewithouttakingexcessiverisksthatcouldhurtaggregateperformance.

Somesimplemodels(Rogers,1988;Giraldeau,Valantone,&Templeton,2002)

predictthatimitationwillnotimprovetheoverallperformanceofagroup,becauseagents

willsimplyuseittotakeadvantageoftheinformationprovidedbyothers,andavoidthe

costsofexploration.Incontrast,wefoundthatparticipantsoftenusedimitation(in

combinationwithinnovationandretentionofprevioussolutionelements)tocumulatively

improveononeanother'ssolutionsandenhancebothindividualandoverallgroup

performance.

Whenweintroducedcontextualfactorsthatcausedimitationtobeeitherdisrupted

(hidingperformanceinformationaboutpeers'solutions)ordiscouraged(chargingasmall

feeforusingasolutionthatapeerhadpreviouslydiscoveredand"protected"),theuseof

innovationincreased,butimprovedperformancedidnotresult.Intheformercase,

participantscouldnotuseimitationtopropagategoodsolutions,andtheincreased

explorationwasessentiallywastedbecausethesearchremainedunfocusedandinefficient.

Inthelattercase,theadditionalexplorationactuallyresultedinanincreaseddiscoveryof

improvedsolutions,butalsothediscoveryofworsesolutionsintheprocess,which

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canceledoutthegains;thecostforimitationmeantthatparticipantsimitatedlessoften

andwerethuslesslikelytobuildononeanother'ssolutions.

8.4.Applicationsandfuturedirections

Inthecontextofscientificandculturalprogress,thereareparallelstothemodelsof

Rogers(1988)andGiraldeau,Valone,andTempleton(2002)mentionedabove,which

predictthatinnovationwillbeinshortsupplyandinefficientlyusedunlessthosewho

innovatecanexcludeothersfromimitatingthemwithoutpermission(e.g.Kitch,1977).

Ourworkshowsthattheabovemodelsareperhapsoverlysimplisticwhenitcomes

tohumansociallearningandexploration.Individualshaveacapacitytouseothers'

innovationsnotjusttoobtainastaticbenefitingoodperformance,buttocreateadynamic

benefitformanybyproducingsequentialimprovements;soadisincentivetoimitate(in

theformofexclusionrightsforinnovators)mayresultinlessproductiveinnovation,not

more.Theworkofothersinthisarea(e.g.Torrance&Tomlinson,2009;Bessen&Meurer,

2008;seeChapters6&7)confirmsthesefindingsandshowsthatthereareother

theoreticalandpracticaldisadvantagestograntingexclusiverightstoknowledge.

Thereisacountervailingmovementtotreatknowledgeasaresourcethatbenefits

fromcommunitymanagementatmultiplescales,ratherthanstrictprivateownershipor

centralizedstatecontrol(Ostrom&Hess,2007).Therearenaturallydebatesbetween

proponentsofthesevariousmethodsofmanagement,butitisclearthatthefutureof

knowledgeisinextricablyboundupinlearninghowtoequitably,efficiently,and

sustainablygoverntheproductsofitspastandpresent.

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Tomasello(1994)contendsthatthecapabilitiesofhumansforselectiveand

cumulativesociallearningconstitutea“ratcheteffect”thatallowsculturetodevelopstably

acrossgenerations,andthatthiseffectmaybeuniquetohumans.Thoughtheexperiments

inthisdissertationpresentagreatlysimplifiedenvironmentforsuchsociallearning,they

confirmedandextendedseveralprevioustheoreticalandempiricalresultsinthefield.

Theconcernsaboutourexperimentsnotedabove(aswellasrelatedworkdiscussed

inpreviouschapters)suggestpotentiallyusefulvariationsofourcoretasks.Forinstance:

useofvariouspracticalknowledgedomainsforsearchandvariouslevelsofexpertise

amongparticipants;useofnoisy(ratherthansimplypresentorabsent)scorefeedback;

variationsinthestructureofthesocialnetworkthatconnectsparticipants;explicitcosts

forinnovationandmoresubstantialincentivesforperformance;andcommunication

amongparticipants,andthereforeopportunitiesforcoordinationoftheirsearchbehavior

andmorestakeholder‐drivengovernanceoftheuseoftheresultingimprovements.

Theresoundingrefrainofthelargebodyofresearchoncommonsdilemmasand

othercollectiveactionproblemsisthatmanycanbesolvedthroughcarefulinvestigation

andmodificationoftherelatedenvironmental,cultural,andinstitutionalvariables,but

thereis"nopanacea,"nouniversalsolutiononwhichwecanrely(Ostrom,2010).

Continuedstudyisnecessary,ofthestructureanddynamicsofhumancollaborative

exploration,thenatureofincentivesandinnovativeeffort,andtheirinteractionas

manifestedinthedynamicsofcreativityinoureconomyandculture.Wepresentourwork

inthehopethatotherswillalsofinditusefulinilluminatingoursharedproblems.

195

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