Reproduction of Hierarchy? A Social Network Analysis of the American Law Professoriate

Reproduction of Hierarchy? A Social Network Analysis of the

American Law Professoriate

Daniel Martin KatzJosh Gubler Jon Zelner

Michael BommaritoEric Provins Eitan Ingall

Motivation for Project


Why Do Certain Paradigms, Histories, Ideas Succeed?



Most Ideas Do Not Persist ....



Function of the ‘Quality’ of the Idea




Function of the ‘Quality’ of the Idea

Social Factors also Influence the Spread of Ideas


Positive Legal Theory

Law Professors are Important Actors



Repositories / Distributors of information



Agents of Socialization






Socialize Future lawyers, Judges & law Professors






Responsible for Developing Particular Legal Ideas(Brandwein (2007) ; Graber (1991), etc.)






Responsible for Developing Particular Legal Ideas(Brandwein (2007) ; Graber (1991), etc.)

Law Professor Behavior is a Important Component of Positive Legal Theory


Social Network Analysis


Method for Tracking Social Connections, etc.


Method for Characterizing Diffusion / Info Flow



Method for Characterizing Diffusion / Info Flow


Method for Ranking Components based upon Various Graph Based Measures

Basic Introduction toSocial Network Analysis

Terminology & Examples

NODES


Actors

NODES


Institutions

Actors

NODES


Institutions

States/Countries

Actors

NODES


Institutions

Firms

States/Countries

Actors

NODES


Institutions

Firms

States/Countries

Actors

NODES

Other


Example: Nodes in an actor- based social Network



Alice



Alice

Bill



Alice

Bill

Carrie



Alice

Bill

Carrie

David



Alice

Bill

Carrie

David

Ellen



Alice

Bill

Carrie

David

Ellen

How Can We Represent The Relevant Social Relationships?


Edges

Alice

Bill

Carrie

David

Ellen

Arcs


Edges

Alice Bill

Carrie

David

Ellen

Arcs


Edges Alice BillCarrie

David

Ellen

Arcs


Alice Bill

David

Carrie

Ellen

A Full Representation of the Social Network


Bill

David

Carrie

Ellen

A Full Representation of the Social Network(With Node Weighting)


Alice

Social Network Analysis of the American Law Professoriate

Cornell University Law School






Building A Graph Theoretic Representation

Cornell

Harvard Penn


Cornell

Harvard Penn


Cornell

Harvard Penn


Cornell

Harvard Penn

Building the Full Dataset





....

Full Data Set

....

7,054 Law Professors! p = {p1, p2, ... p7240}

Full Data Set

....

7,054 Law Professors! p = {p1, p2, ... p7240}

184 ABA Accredited Institutions n = {n1 , n2, … n184}

Full Data Set

....

Visualizing a Full Network





Zoomable Visualization Available @ http://computationallegalstudies.com/

http://computationallegalstudies.com


Zoomable Visualization Available @ http://computationallegalstudies.com/



A Graph-Based Measure of Centrality

Hub Score

Hub Score

Similar to the Google PageRank™ Algorithm

Measure who is important?

Measure who is important to who is important?

Run Analysis Recursively...

Hub Score

Score Each Institution’s Placements by Number and Quality of Links

Normalized Score (0, 1]

Similar to the Google PageRank™ Algorithm

Measure who is important?

Measure who is important to who is important?

Run Analysis Recursively...

Hub Score Rank

US News Peer

Assessment Hub

Score Institution

1 1 1.0000000 Harvard2 1 0.9048631 Yale3 5 0.8511497 Michigan4 4 0.7952253 Columbia5 5 0.7737389 Chicago6 8 0.7026757 NYU7 1 0.6668868 Stanford8 8 0.6607399 Berkeley9 10 0.6457157 Penn

10 10 0.6255498 Georgetown11 5 0.5854464 Virginia12 14 0.5014904 Northwestern13 10 0.4138745 Duke14 10 0.4075353 Cornell15 15 0.3977734 Texas16 28 0.3787268 Wisconsin17 19 0.3273598 UCLA18 24 0.2959581 Illinois19 28 0.2919847 Boston University20 28 0.2513371 Minnesota21 24 0.2403289 Iowa22 28 0.2275534 Indiana23 19 0.2235015 George

Washington24 16 0.2174677 Vanderbilt25 41 0.2012442 Florida

Hub Score Rank

US News Peer

Assessment Hub

Score Institution

26 24 0.1999686 UC Hastings27 34 0.1974877 Tulane28 28 0.1749897 USC29 35 0.1702638 Ohio State30 24 0.1586516 Boston College31 72 0.1543831 Syracuse32 19 0.1537236 UNC33 56 0.1525355 Case Western34 82 0.1511569 Northeastern35 19 0.1428239 Notre Dame36 56 0.1286375 Temple37 82 0.1232289 Rutgers Camden38 56 0.1227421 Kansas39 64 0.1213358 Connecticut40 47 0.1198901 American41 34 0.1162101 Fordham42 64 0.1150860 Kentucky43 106 0.1148082 Howard44 47 0.1125957 Maryland45 28 0.1101975 William & Mary46 56 0.1058079 Colorado47 19 0.1041129 Emory48 17 0.1031490 Washington & Lee49 72 0.1027442 Miami50 103 0.1006172 SUNY Buffalo

Hub Scores

Hub Score Rank US News Peer

Assessment Score Hub

Score Institution

26 24 0.1999686 UC Hastings

27 34 0.1974877 Tulane

28 28 0.1749897 USC

29 35 0.1702638 Ohio State

30 24 0.1586516 Boston College

31 72 0.1543831 Syracuse

32 19 0.1537236 UNC

33 56 0.1525355 Case Western

34 82 0.1511569 Northeastern

35 19 0.1428239 Notre Dame

36 56 0.1286375 Temple

37 82 0.1232289 Rutgers Camden

38 56 0.1227421 Kansas

39 64 0.1213358 Connecticut

40 47 0.1198901 American

41 34 0.1162101 Fordham

42 64 0.1150860 Kentucky

43 106 0.1148082 Howard

44 47 0.1125957 Maryland

45 28 0.1101975 William & Mary

46 56 0.1058079 Colorado

47 19 0.1041129 Emory

48 17 0.1031490 Washington & Lee

49 72 0.1027442 Miami

50 103 0.1006172 SUNY Buffalo



Score Institution

26 24 0.1999686 UC Hastings

27 34 0.1974877 Tulane

28 28 0.1749897 USC

29 35 0.1702638 Ohio State


31 72 0.1543831 Syracuse32 19 0.1537236 UNC

33 56 0.1525355 Case Western

34 82 0.1511569 Northeastern

35 19 0.1428239 Notre Dame

36 56 0.1286375 Temple


38 56 0.1227421 Kansas


40 47 0.1198901 American

41 34 0.1162101 Fordham

42 64 0.1150860 Kentucky

43 106 0.1148082 Howard

44 47 0.1125957 Maryland

45 28 0.1101975 William & Mary

46 56 0.1058079 Colorado

47 19 0.1041129 Emory


49 72 0.1027442 Miami

50 103 0.1006172 SUNY Buffalo



Score Institution

26 24 0.1999686 UC Hastings

27 34 0.1974877 Tulane

28 28 0.1749897 USC

29 35 0.1702638 Ohio State


31 72 0.1543831 Syracuse32 19 0.1537236 UNC

33 56 0.1525355 Case Western

34 82 0.1511569 Northeastern35 19 0.1428239 Notre Dame

36 56 0.1286375 Temple


38 56 0.1227421 Kansas


40 47 0.1198901 American

41 34 0.1162101 Fordham

42 64 0.1150860 Kentucky

43 106 0.1148082 Howard

44 47 0.1125957 Maryland

45 28 0.1101975 William & Mary

46 56 0.1058079 Colorado

47 19 0.1041129 Emory


49 72 0.1027442 Miami

50 103 0.1006172 SUNY Buffalo



Score Institution

26 24 0.1999686 UC Hastings

27 34 0.1974877 Tulane

28 28 0.1749897 USC

29 35 0.1702638 Ohio State


31 72 0.1543831 Syracuse32 19 0.1537236 UNC

33 56 0.1525355 Case Western


36 56 0.1286375 Temple

37 82 0.1232289 Rutgers Camden38 56 0.1227421 Kansas


40 47 0.1198901 American

41 34 0.1162101 Fordham

42 64 0.1150860 Kentucky

43 106 0.1148082 Howard

44 47 0.1125957 Maryland

45 28 0.1101975 William & Mary

46 56 0.1058079 Colorado

47 19 0.1041129 Emory


49 72 0.1027442 Miami

50 103 0.1006172 SUNY Buffalo



Score Institution

26 24 0.1999686 UC Hastings

27 34 0.1974877 Tulane

28 28 0.1749897 USC

29 35 0.1702638 Ohio State


31 72 0.1543831 Syracuse32 19 0.1537236 UNC

33 56 0.1525355 Case Western


36 56 0.1286375 Temple



40 47 0.1198901 American

41 34 0.1162101 Fordham

42 64 0.1150860 Kentucky

43 106 0.1148082 Howard44 47 0.1125957 Maryland

45 28 0.1101975 William & Mary

46 56 0.1058079 Colorado

47 19 0.1041129 Emory


49 72 0.1027442 Miami

50 103 0.1006172 SUNY Buffalo



Score Institution

26 24 0.1999686 UC Hastings

27 34 0.1974877 Tulane

28 28 0.1749897 USC

29 35 0.1702638 Ohio State


31 72 0.1543831 Syracuse32 19 0.1537236 UNC

33 56 0.1525355 Case Western


36 56 0.1286375 Temple



40 47 0.1198901 American

41 34 0.1162101 Fordham

42 64 0.1150860 Kentucky

43 106 0.1148082 Howard44 47 0.1125957 Maryland

45 28 0.1101975 William & Mary

46 56 0.1058079 Colorado

47 19 0.1041129 Emory


49 72 0.1027442 Miami

50 103 0.1006172 SUNY Buffalo

Distribution of Social Authority

0

200

400

600

800

1,000

Harvard Yale Michigan Columbia Chicago NYU Stanford Berkeley UVAGeorgetownPennNorthwesternTexas Duke UCLA Cornell

Wisconsin BU IllinoisMinnesota

Top 20 Institutions (By Raw Placements)

!

!

Highly Skewed Nature ofLegal Systems

!


Katz & Stafford 2010

!



!


Smith 2007


!


Smith 2007


!


Smith 2007

Post & Eisen 2000Katz & Stafford 2010

!

Implications for Rankings


Rankings only Imply Ordering ( >, =, < )



End Users tend to Conflate Ranks with Linearized Distances Between Units

(Tversky 1977)



End Users tend to Conflate Ranks with Linearized Distances Between Units

(Tversky 1977)

Non-Stationary Distances Between Entities

Both Trivial and Large DistancesLinearity Heuristic Often WorksAssuming Linearity Can Prove Misleading

Computational Model of Information Diffusion

Why Computational Simulation?


History only Provides a Single Model Run


History only Provides a Single Model Run

Computational Simulation allows ... Consideration of Alternative “States of the world”

Evaluation of Counterfactuals



We Apply a simple Disease Model to Consider the Spread of Ideas, etc.


We Apply a simple Disease Model to Consider the Spread of Ideas, etc.

Clear Tradeoff Between Structural Position in the Network and “Idea Infectiousness”

A Basic Description of the Model


Consider a Hypothetical Idea Released at a Given Institution



Infectiousness Probability = p




Infect neighbors, neighbors-neighbors, etc.




Two Forms Diffusion...Direct SocializationSignal Giving to Former Students

Infect neighbors, neighbors-neighbors, etc.

Channels of Diffusion

Lots of Channels of Information Diffusion Among Legal Academics




Legal Socialization / Training


Judicial Decisions, Law Reviews, Other Materials





Academic Conferences, Other Professional Orgs






SSRN, Legal Blogosphere, etc.






SSRN, Legal Blogosphere, etc.


Other Channels of Information Dissemination


A Sample Run of the Model















Run a Simulationon Your Desktop




(Requires Java 5.0 or Higher)






http://computationallegalstudies.com/2009/04/22/the-revolution-will-not-be-televised-but-will-it-come-from-harvard-or-yale-a-network-analysis-of-the-american-law-professoriate-part-iii/






From a Single Run to Consensus Diffusion Plot


Netlogo is Good for Model Demonstration







http://ccl.northwestern.edu/netlogo/





Regular Programming Language TypicallyRequired for Full Scale Implementation







We Used Python







We Used Python







We Used Python


http://www.python.org/



http://www.python.org





We Used Python


http://www.python.org/

Object Oriented Programming Language







Repeated the Diffusion Simulation



Hundreds of Model Runs Per School




Yielded a Consensus Plot for Each School




Yielded a Consensus Plot for Each School

Results for Five Emblematic SchoolsExponential, linear and sub-linear

!

Computational Simulation of Diffusion upon the Structure of the American Legal Academy

Some Potential Model Improvements?

Differential Host Susceptibility




Countervailing Information / Paradigms



Countervailing Information / Paradigms

S I R Model Susceptible-Infected-Recovered

Directions for Future Research


Longitudinal Data Hiring/Placement/LateralsCurrent Collecting Data



Database Linkage to Articles/CitationsWorking with Content Providers



Database Linkage to Articles/CitationsWorking with Content Providers

Empirical Evaluation of SimulationComputational LingusiticsText Mining, Sentiment Coding

Thanks for Support

News & Politics

Reproduction of Hierarchy? A Social Network Analysis of the American Law Professoriate