Using Social Impact Theory to simulatelanguage changeroland/SLANG12/presentations/Handout-3… · Using Social Impact Theory to simulatelanguage change Daniel Nettle ... ‘culturalparents‘

27.06.2012

1

Using Social Impact Theory to

simulate language change

Daniel Nettle

(1998)

26.06.2012 1Mareike Gann

• Introduction

• Social Impact Theory

• The simulation

• Social selection in the simulation

• Functional selection in the simulation

• Conclusion

• Personal opinion

26.06.2012 Mareike Gann 2

Outline


Introduction

• A model would help us to learn more about language change

dynamics.

• Existing model: cultural evolution model

• This model is inspired by population genetics and biological evolution.

• Problem: There are more than two (or another fixed number of)

‘cultural parents‘ in language learning. The process of language

acquisition is very long, so the learner samples a wide range of

sources. Influences depend on social factors.

• Variants of language change:

• imperfect learning

• accidental variants of linguistic performance


Introduction – the threshold problem

• Linguistic ‘mutation‘ will not be adopted by the next

generation because of the great number of cultural parents.

� No change through imperfect learning

� New mutants can only become fixed if they pass a

threshold of frequency

• New variants can spread, otherwise there would be

homogeneity after a few generations.

�Possible thanks to different weights of input

�Bias towards new variant because of social influence or

easiness of acquisition


Introduction – social/functional selection

• Social selection: Learners of language do not simply pick up

the most common norms. They are biased towards particular

people and their way of speaking.

� Membership of a social group

• Functional selection: Learners may have biases towards

particular linguistic items because of their simplicity.

� A new variant might overcome the threshold problem. This

would be a linguistic change.


Social Impact Theory

• Psychological model by Latané(1981):

� Attributes or behaviours of an individual are influenced by

others according to:

• Strength: social status of the people

• Immediacy: social distance to the learner

• Number

• In linguistic matters the different complexity of two variants is

also important.

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• General formula:

• i is the impact of the variant

• b is the bias towards the variant

• f is the function

• S is the social status

• D is the social distance

• N is the number of persons using the variant

• Specification of impact function:

• si is the social status of the ith individual with that variant

• di is the social distance of this ith individual

• a is the increasing of impact if more people use this variant/

importance of conformity in language



• Two competing linguistic variants p and q:

� the variant with the higher impact i will be adopted

• This model becomes an interesting approach to language

change by setting up a dynamic population of speaker.

• A population of 400 people in a 20 by 20 grid is built.

� no representation of spatial structure, rather a social structure

� Individuals pass through 5 lifestages/ there are 5 ages

�Horizontal: familial ties; Vertical: own generation

� After each lifestage all ages are increased by one, 5 dies � new 1

� At age 1 and 2 indiviuals learn from their surrounding, influenced by

all others except those at age 1.

Imperfect learning /mutation rate 5%

� No more variant changes at age 3, 4 and 5.


The simulation

5 4 3 2 1 1 2 3 4 5

5 4 3 2 1 1 2 3 4 5

5 4 3 2 1 1 2 3 4 5


• No functional and social bias (b=1, si=1, di=1) , a=1,

The simulation - Basic results


threshold problem:

• q occurs, but cannotspread because of theinfluential majorityusing p

• � modifications of basic simulation

The simulation - Basic results


The simulation – Varying the constant a

Lowering a < 1 :

impact of variant

rises less than

linearly with

increasing number of

persons using it

�Reduction of

importance of large

numerical majorities

in the learning

process

a = 0.5

�q able to increase

its frequency

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The simulation – Varying the constant a

q establishes in one

part of the space

�50-50 with a <= 0.5,

so dialects can develop

�Basically all p with

0.5 < a <= 1

�Problem: This does

not ressemble reality

�a=0.8 , so q can

occasionally

spread26.06.2012 Mareike Gann 14

The simulation – Varying the mutation rate

Modification of rate of imperfect learning decreases

homogeneity� no norm change


The simulation – Varying the weighting of social distance

so far: net impact of an

individual: 1/di²

�Increasement of

distance power:

individuals with more

distance have even less

impact, but nearer

agents have

comparatively much

more influence

�dialects can develop


Social selection

Distribution of status follows a Poisson curve � only a small number

of superinfluential individuals, status value of 1 to 20

A:

Mutation rate 5%, a= 0.8

�No language change

B:

Implementation of hyperinfluential

individuals (status 100)

� Rare variant can become norm


Functional selection

Social selection, mutation rate 5%, a = 0.8

Varying bq , the bias

towards the variant q

�bq =0.5: q never

spreads

�bq =1: rapid

changes

�bq =2: q quickly

spreads and stays



Variations of the bias to q

� Even small biases above 1 help q to spread

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No social

selection

(si=1, di=1),

bias towards q:

bq=2

� No language change: functional bias can only affect the direction of

language change26.06.2012 Mareike Gann 20

Conclusion

• The learner samples over the language being used in his

whole community. He weights different sources according to

their social status and distance.

• Separate dialects develop by manipulating the distance

parameters or by manipulating the importance learners give

to conformity ( a ).

• Role of functional bias: Even a small bias is sufficient to

determine which of the two variants will spread. It cannot

produce a language change alone, but it can affect the

direction of change.


Personal opinion

• I think it is nice that we can see, that without the

consideration of different weightening of input language

change can‘t be simulated. Therefore, the importance of

social impact is showed.

• This simulation is a good beginning of simulation of language

change, but there are still many factors that must be

considered like the size of a speech community and the

contact to other speech communities.

Written by: Jinyun Ke, Tao Gong and William S-Y Wang (2007)

Presented by: Corinna Huettel

1. Introduction

2. Language change as a diffusion process

3. The model

4. The effect of different types of networks

5. Effect of two types of learners

6. Effect of different population size

7. Conclusion

8. Personal statement

• Social networks determining factor in languages

• Sociolinguistic studies of social networks focus on:�Small communities

�Relation between individuals

�Example: three inner-city communities in Belfast

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• Multiple relationships within individuals�Relatives�Neighbors�Friends�Colleagues

• Different degrees of integration

• Linguistic behaviors related to integrity into network�The more integrated a person is, the more (s)he adapts to speech norms

• Very few empirical data have actually been able to show the effect of social networks over a long time

• It‘s hardly possible to get the structure of large communities�Can be done by computer simulations

• Parameters can be manipulated due to computer simulations (population size, connectivity...)

• BUT: Computer models cannot consider the actual population structure or regular or random networks

• Recent studies show that large-scale networks (internet, friendship...) are not regular or random

• Two features discovered:�Scale-free

�Small-world

� Examination of the effect of social networks on

the dynamics and outcome of language change

• Language change = diffusion process of some new linguistic elements in language communities

• Language learner samples a (large) part of the language community in his peer group or older generations, NOT younger generations�New innovations unlikely learned by next generation: „Threshold Problem“

• Overcoming the threshold:�Functional selection: a functional bias towards the innovation

�Social selection: speakers with higher social impact favor the learning

• Model to study the threshold problem (by Nettle):�Simulation of attitude changes in social groups�Population structured in age and social status�Learner chooses one linguistic variant by evaluating their impact in the community

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• Model to study the threshold problem (by Nettle):�Shorter social distance/higher social status =>stronger impact on learner

�Innovation with small functional advantage has a high chance to spread

�Conclusion: functional biases maybe affect the direction of language change, but may not provide the conditions for change

�Challenge to explain „changes from below“: many changes start in upper working class or lower middle class

• Population represented as network with Nnodes (agents)

• Two linguistic states�Unchanged form of innovation: U

�Changed form of innovation : C

• Age structure from 1 (infants) to 5 (adults)

• 1+2 learners; 3-5 teachers

• Old agents get replaced

• Illustration, how a learner might learn from neighbors:

F(U)=fuqu

F(C)=fcqc

• U and C in the input=> learning form with higher fitness

• Fitness measured by:�Function of incorporating the functional value (fu/fc) �Frequency in the learner’s neighborhood (qu/qc)

• State of the learner:

• Example:�Network of 10 agents�Learner connected with 4 agents, 3 use U, 1 uses C�Functional values: U=1; C=4 => F(U)=3; F(C)=4

Learner will learn C-form

• Example:�Assumption: fu=1

�Using parameter functional bias ß, measuring functional advantage of C/U: ß=fc/fu

• Diffusion process compared in 4 different kinds of network structures:�Random

�Regular

�Small-world

�Scale-free

• Functional bias=20; Innovators=1• The diffusion is successful in all types of networks,but the curves look different

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• Functional bias=10; Innovators=10• The diffusion rate in small-world networks now changed,because the number of short-cut relations are smaller

• Functional bias=2; Innovators=100• Runs with unsuccessful diffusion

• Between 3 to 7 regular and small-world networks have a higherprobability of diffusion rate than the others• Small-world and regular networks: high success probability, but slowdiffusion rate• Random and scale-free networks: high diffusion rate, but no slowsuccess probability

• Learner learn from all connected neighbors at age stage 1+2

• Two types:�Categorical: adopts form with higher impact

�Probabilistic: adopts both forms and uses them proportional to their impact

• Probabilistic learners make language change so frequent

• If the learners are all probabilistic diffusion is possible • In small-world networks the rate is higher but it takeslonger

• The more probabilistic learners there are, the fasterdiffusion there is

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• Regular and small-world networks: high success probability, but slow diffusion rate

• Random and scale-free networks: fast diffusion rate, but lower success probability

• This model shows that there is a very high probability of linguistic change as long as there is at least a small number of probabilistic learners

• I think the model is very abstract, because the study is based on a computer simulation not on real world community structures

• I now know some models that may explain language innovations better

• It is interesting that it depends on the type of learner if an innovation spreads

SLANG - PresentationSLANG - Presentation

Connection Science - Exploring social structure effect on language

evolution based on a computational modelTao Gong a; James W. Minett a; William S. -Y. Wang

Presented by: Kathrin Adlung

OutlineOutline● Introduction

● The representation and acquisition of linguistic rules

● Communication

● Evaluating the performance

● The Experiment

● Experiments

● Experiment 1

● Experiment 2

● Experiment 3

● Conclusion: Experiment 1 & 2

● Conclusion: Experiment 3

● Overall conclusion

IntroductionIntroduction

This paper, (instead of modeling like

● Livingstone (all agents were arranged in a single row, the ends of which were disconnected. Communications among agents were

limited by predefined neighbourhoods based on distance.)

● or Nettle (social structure was modelled as a weighted, regular network (a network whose nodes have an equal number of weighted edges connecting to other nodes).))

concentrates on the probabilities that individualsparticipate in communications and discuss their effect on

language evolution.

The representation and acquisition The representation and acquisition

of linguistic rulesof linguistic rules

● Meaning-utterance mappings (M-U mappings)

● Type 1: ‘Pr1<Ag>

● ‘run<wolf>’ meaning ‘a wolf is running’

● Type 2: ‘Pr2<Ag, Pat>’,

● ‘chase<wolf, sheep>’ meaning ‘a wolf is chasing

a sheep’

The representation and acquisition The representation and acquisition

of linguistic rulesof linguistic rules● The rule based system

● Lexical rules

● Holistic rules

● Compositional rules

● Syntactic rules

● Local ordrs between Strings of two sets

● Syntactic categories

● Syntactic role

● List of lexical rules

CommunicationCommunication

● Environmental cues

● Realibility of Cues (RC)

● Communication

● multiple rounds of of utterance exchange

● Activation of lecical rules

● Posetive or negative feedback

● No check between intended meaning and comprehended one

Evaluating the performanceEvaluating the performance

● Understanding Rate (UR)

● The higher the rate, the higher the understandability

● Convergence Time (CT)

● The rounds needed to achieve a certain UR

The ExperimentThe Experiment

● In the simulation

● Agents

● Share holistic rules

● Language

● 12 compositional rules

● Syntactic rules (SV, VO, SO)

● Global order (SVO)

● Experiment

● 20 simulations

ExperimentsExperiments

● 1. Experiment: a community with a single popular agent is simulated, and this agent’s popularity is regulated by PR

● 2. Experiment: a community with a predefined distribution of individuals’popularities is simulated

● 3. Experiment: a situation where agents from two communities interact with each other is simulate

Experiment 1Experiment 1

● Simulation

● 10-agent community

● Setup

● 1 popular agent, 9 other agents

● Number of communication

● 6000 → 600 rounds

● Forms of communication

● Communication between popular agent and other agent

● Communication not only involving the popular agent


● Communication not only involving the popular agent

● Probability 1-PR

● PR: Intervall [0,1 1,0]

● 0,1 → equal communication

● 1,0 → only communication with popul aragent

● The effects

● The accelaration effect

● The PA connectsto many others and provides a conduct to exchange communication

● The deceleration effect

● For efficiently transmitting information, the hub has to be stable

The statistical results in Experiment 1 on language emergence: the UR (a) and CT (b) of the emergent languages under different PR. The distance between a pair of error bars above and below a data point is twice of the standard deviation


● Simulation

● the distribution of all agents’ popularities and the study the effect of individuals’ popularities

● Setup

● 10-agent community, distribution of all agents’ popularities

● The distribution of agents’ popularities

● power-law distribution

– y = ax^−λ

– a → a scale parameter

– x → an element or interaction

in a given phenomenon,

– y → frequency of this element or interaction.

The individuals’ popularities in different power-law distributions. The top figure is in normal axes, and the bottom one in log–log axes.


● Simulation

● Agents of two communities

● Setup

● Each community has a 10-agent group

● Number of communication

● 6000 (600 rounds)


● Own communal language with high UR

● Mutal understanding determined by the percentage of inter-community communication

The statistical results in Experiment 3 on language emergence: the UR (a) and CT (b) of the communal languages in different communities under various degrees of linguistic contact.

Conclusion: Experiment 1 & 2Conclusion: Experiment 1 & 2

● Acceleration & decleration effect of popular agent

● Neither totally biased nor unbiased learning can result in a good level of understanding

● Impact on language evolution of individuals having power-law distributed popularities

● Efficient communication → λ value of power-law not very high

Conclusion: Experiment 3Conclusion: Experiment 3

● Learning between two communities

● Linguistic contact can affect the convergence of a communal language

● No social structure → control the probabilities for individuals to participate in communications

● studying the effect of social structure on language evolution

● social structures with various connection patterns may share similar characteristics that can cast their influence on linguistic

exchange.●

Overall conclusionOverall conclusion

● Can help the to study the effect od social structure on language evolution

● The probabilities that individuals participate in communications should be frequently updated

● PR, Individual’s Popularity, IntraRate, and InterRate only determine the probability for agents to participate in communications not the roles

● the roles can affect language evolution

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Using Social Impact Theory to simulatelanguage changeroland/SLANG12/presentations/Handout-3… · Using Social Impact Theory to simulatelanguage change Daniel Nettle ... ‘culturalparents‘