Law as a Complex System?

Hustle and Flow: A Social Network Analysis of the American Federal Judiciary

Daniel Martin Katz & Derek K. Stafford

University of Michigan, Department of Political Science

BA Model Simulated in Net Logo

Coming Soon

BA Preferential Attachment Model Ranking the Jurists

Acknowledgements:

We would like to thank the John M. Olin Center for Law and Economics at the University of Michigan for its support of this project.

For further information:

Please contact dmartink@umich.edu

More information on this and related projects can be obtained at:

www.sitemaker.umich.edu/dankatz

The Hiring and Placement of the American Law Professoriate

Daniel Martin Katz

Joshua Gubler

Eric Provins

Eitan Ingall

The University of Michigan

Department of Political Science

Kamada-Kawai* Kamada-Kawai* Energized Judicial Social NetworkEnergized Judicial Social Network

Complex Systems PropertiesComplex Systems Properties Information in the InteractionsInformation in the Interactions Emergence, Convergence, Self-Organization, Path DependenceEmergence, Convergence, Self-Organization, Path Dependence Positive and Negative FeedbackPositive and Negative Feedback Non-Linear Dynamics including possible Phase Transitions Non-Linear Dynamics including possible Phase Transitions

Network Science Network Science Mapping Interactions between Agents in a Complex Adaptive SystemMapping Interactions between Agents in a Complex Adaptive System Built upon mixture of linear algebra, graph theory and statistics Built upon mixture of linear algebra, graph theory and statistics

A Proxy for Judicial Interactions?A Proxy for Judicial Interactions? Hypothesis: In the aggregate, there is information about reputation, Hypothesis: In the aggregate, there is information about reputation,

prestige, influence and esteem of jurists embedded in the traffic of prestige, influence and esteem of jurists embedded in the traffic of clerksclerks

Collected 19,000 Article III Law Clerk “Events” (1995-2004)Collected 19,000 Article III Law Clerk “Events” (1995-2004) Mapped the Traffic of Clerks Between All Article III Jurists Mapped the Traffic of Clerks Between All Article III Jurists

States of the WorldFruchterman-Reingold* Fruchterman-Reingold*

Energized Judicial Social NetworkEnergized Judicial Social Network

Thirty Most Central Federal Judges

Jurist Centrality

Alito_Samuel_A 0.023137111

Boudin_Michael 0.094981577

Brunetti_Melvin_T 0.031860909

Cabranes_Jose_A 0.040859744

Calabresi_Guido 0.132071003

Easterbrook_Frank_H 0.029115868

Edwards_Harry_T 0.101003638

Flaum_Joel_M 0.023137202

Fletcher_William_A 0.034383907

Garland_Merrick 0.045101794

Ginsburg_Douglas_H 0.106655149

Higginbotham_Patrick_E 0.038283304

Jones_Edith_H 0.051847613

Kozinski_Alex 0.199448153

Leval_Pierre_N 0.061667539

Luttig_J_Michael 0.460086375

Niemeyer_Paul_V 0.057598972

OScannlain_Diarmuid 0.12676303

Posner_Richard 0.119017709

Randolph_Raymond 0.04502409

Reinhardt_Stephen_R 0.039234543

Rymer_Pamela_Ann 0.035610044

Sentelle_David_B 0.102452911

Silberman_Laurence_H 0.224592733

Tatel_David_S 0.1153377

Wald_Patricia_M 0.033537262

Wallace_Clifford 0.034474947

Wilkinson_J_Harvie 0.211140835

Williams_Stephen_F 0.090441285

Winter_Ralph_K 0.049458759

Erdos-RenyiBernoulli Graph

Markov Clustered Network

Watts-Strogatz Small World

Barabási-Albert (BA) Preferential

Attachment

Visualizations

*Tomihisa Kamada & Satoru Kawai, An Algorithm for Drawing General Undirected Graphs, 31 Information Processing Letters 7 (1989) *Thomas Fruchterman & Edward Reingold, Graph Drawing by Force-Directed Placement, 21 Software Practice & Experience 1129 (1991).

Power Law Degree

Distribution Implies a Process

Preferential Attachment*

≅

* Laszlo Barabasi & Reka Albert, Emergence of Scaling in Random Networks, 286 Science 509 (1999).* Reka Albert & Laszlo Barabasi, Statistical Mechanics of Complex Networks, 74 Review of Modern Physics 47 (2002).

p(x) p(x) ∝ ∝ x x −α−α

KleinbergAuthority Scores*

*Jon M. Kleinberg, Authoritative Sources in a Hyperlinked Environment, 668 Proceedings of ACM-SIAM Symposium of Discrete Algorithms (1999)

Log/Log Graph of Degree Distributions

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2.5

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3.5

Log Judges

Log

Deg

ree

Degree Frequency Disributions

0

100

200

300

400

500

600

700

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33

Degree

Judg

es circ judges

district judges

aggregate

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

Derek Stafford, Daniel Katz & Eric Provins, Social Architecture, Judicial Peer Effects and Law’s Evolution: Toward a Positive Theory of Judicial Social Structure, 23 Ga. St. U. L. Rev ___ (2008

Forthcoming)

Symposium Issue-- Dynamical Jurisprudence: Law as a Complex System