Network Analysis and Law: Introductory Tutorial @ Jurix 2011 Meeting (Vienna)

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Daniel Martin Katz (Illinois Tech - Chicago Kent) & Michael Bommarito (Computational Legal Studies.com) Present Network Analysis and Law: Introductory Tutorial @ Jurix 2011 (Vienna)

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Network Analysis and Law: Introductory Tutorial @ Jurix 2011 Meeting (Vienna)

  1. 1. Network Analysis and the Law Daniel Martin Katz Illinois Tech Chicago Kent College of Law Michael J. Bommarito II Center for Study of Complex Systems Jurix 2011 Tutorial @ Universität Wien !
  2. 2. My Background Associate Professor of Law Illinois Tech - Chicago Kent Law Former NSF IGERT Fellow, University of Michigan Center for the Study of Complex Systems (2009-2010) PhD Political Science & Public Policy University of Michigan (2011) JD University of Michigan Law School (2005)
  3. 3. My Background Former NSF IGERT Fellow, University of Michigan Center for the Study of Complex Systems PhD Pre-Candidate Dept. of Political Science University of Michigan Masters Degree Financial Engineering University of Michigan
  4. 4. Outline of Our Session Network Analysis: An Extended Primer Network Analysis & Law The Frontier of Network Analysis & Law Legal Elites Diffusion and other Related Processes Legal Doctrine and Legal Rules Advanced Network Science Topics Community Detection ERGM / P* Models Social Epidemiology Distance Measures for Dynamic Citation Networks Dynamic Community Detection The Judicial Collaborative Filter (Judge Aided Info Retrevial)
  5. 5. Network Analysis: An Extended Primer
  6. 6. Introduction to Network Analysis What is a Network? What is a Social Network? Mathematical Representation of the Relationships Between Units such as Actors, Institutions, Software, etc. Special class of graph Involving Particular Units and Connections
  7. 7. Introduction to Network Analysis Interdisciplinary Enterprise Applied Math (Graph Theory, Matrix Algebra, etc.) Statistical Methods Social Science Physical and Biological Sciences Computer Science
  8. 8. Social Science For Images and Links to Underlying projects: http://jhfowler.ucsd.edu/ 3D HiDef SCOTUS Movie Co-Sponsorship in Congress Spread of Obesity Hiring and Placement of Political Science PhD’s
  9. 9. Social Science The 2004 Political Blogosphere (Adamic & Glance) High School Friendship (Moody) Roll Call Votes in United States Congress (Mucha, et al)
  10. 10. Physical and Biological Sciences For Images and Links to Underlying projects: http://www.visualcomplexity.com/vc/
  11. 11. Computer Science Mapping of the Code Networks are ways to represent dependancies between software
  12. 12. Computer Science Internet is one of the largest known and most important networks
  13. 13. Computer Science Mapping the Iranian Blogsphere http://cyber.law.harvard.edu/publications/2008/Mapping_Irans_Online_Public
  14. 14. Primer on Network Terminology
  15. 15. Terminology & Examples Institutions Firms States/Countries Actors NODES Other
  16. 16. Example: Nodes in an actor- based social Network Alice Bill Carrie David Ellen How Can We Represent The Relevant Social Relationships? Terminology & Examples
  17. 17. Edges Alice Bill Carrie David Ellen Arcs Terminology & Examples
  18. 18. Edges Alice Bill Carrie David Ellen Arcs Terminology & Examples
  19. 19. Edges Alice Bill Carrie David Ellen Arcs Terminology & Examples
  20. 20. Alice Bill David Carrie Ellen A Full Representation of the Social Network Terminology & Examples
  21. 21. Bill David Carrie Ellen Terminology & Examples Alice A Full Representation of the Social Network (With Node Weighting)
  22. 22. Bill David Carrie Ellen A Full Representation of the Social Network (With Node Weighting and Edge Weighting) Terminology & Examples Alice
  23. 23. A Survey Based Example “Which of the above individuals do you consider a close friend?” Image We Surveyed 5 Actors: (1) Daniel, (2) Jennifer, (3) Josh, (4) Bill, (5) Larry
  24. 24. From an EdgeList to Matrix 1 2 3 4 5 --------------------------- Daniel (1) 0 1 1 1 1 Jennifer (2) 1 0 1 0 0 Josh (3) 0 1 0 1 1 Bill (4) 0 0 0 0 0 Larry (5) 1 1 1 1 0 *Directed Connections (Arcs) 13 1 2 1 3 1 4 1 5 2 1 2 3 3 4 3 5 3 2 5 1 5 4 5 3 5 2 ROWS è COLUMNS *How to Read the Edge List: (Person in Column 1 is friends with Person in Column 2)
  25. 25. 1 2 3 4 5 --------------------------- Daniel (1) 0 1 1 1 1 Jennifer (2) 1 0 1 0 0 Josh (3) 0 1 0 1 1 Bill (4) 0 0 0 0 0 Larry (5) 1 1 1 1 0 From a Survey to a Network
  26. 26. A Quick Law Based Example of a Dynamic Network
  27. 27. United States Supreme Court To Play Movie of the Early SCOTUS Jurisprudence: http://vimeo.com/9427420 Documentation is Available Here: http://computationallegalstudies.com/2010/02/11/the-development-of-structure-in-the-citation-network-of-the- united-states-supreme-court-now-in-hd/
  28. 28. Some Other Examples of Networks
  29. 29. Consumer Data Knowing Consumer Co-Purchases can help ensure that “Loss Leader” Discounts can be recouped with other purchases
  30. 30. Corporate Boards http://www.theyrule.net/
  31. 31. Transportation Networks We might be interested in developing transportation systems that are minimize total travel time per passenger
  32. 32. Power Grids We might be interested in developing Power Systems that are Globally Robust to Local Failure
  33. 33. Campaign Contributions Networks http://computationallegalstudies.com/tag/110th-congress/
  34. 34. The United States Code http://computationallegalstudies.com/ + Hierarchical Structure
  35. 35. Some Recent Network Related Publications Special Issue: Complex systems and Networks July 24, 2009 Special 90th anniversary Issue: May 7, 2007
  36. 36. History of Network Science
  37. 37. The Origin of Network Science is Graph Theory The Königsberg Bridge Problem the first theorem in graph theory Is It Possible to cross each bridge each and only once?
  38. 38. The Königsberg Bridge Problem Leonhard Euler (Pronounced Oil-er) proved that this was not possible Is It Possible to cross each bridge each and only once?
  39. 39. Eulerian and Hamiltonian Paths Eulerian path: traverse each edge exactly once If starting point and end point are the same: only possible if no nodes have an odd degree each path must visit and leave each shore If don’t need to return to starting point can have 0 or 2 nodes with an odd degree Hamiltonian path: visit each vertex exactly once
  40. 40. Modern Network Science
  41. 41. Moreno, Heider, et. al. and the Early Scholarship Focused Upon Determining the Manner in Which Society was Organized Developed early techniques to represent the social world Sociogram/ Sociograph Obviously did not have access to modern computing power
  42. 42. Stanley Milgram’s Other Experiment Milgram was interested in the structure of society Including the social distance between individuals While the term “six degrees” is often attributed to milgram it can be traced to ideas from hungarian author Frigyes Karinthy What is the average distance between two individuals in society?
  43. 43. Stanley Milgram’s Other Experiment NE MA
  44. 44. Six Degrees of Separation? NE MA Target person worked in Boston as a stockbroker 296 senders from Boston and Omaha. 20% of senders reached target. Average chain length = 6.5. And So the term ... “Six degrees of Separation”
  45. 45. Six Degrees Six Degrees is a claim that “average path length” between two individuals in society is ~ 6 The idea of ‘Six Degrees’ Popularized through plays/movies and the kevin bacon game http://oracleofbacon.org/
  46. 46. Six Degrees of Kevin Bacon
  47. 47. Visualization Source: Duncan J. Watts, Six Degrees Six Degrees of Kevin Bacon
  48. 48. But What is Wrong with Milgram’s Logic? 150(150) = 22,500 150 3 = 3,375,000 150 4 = 506,250,000 150 5= 75,937,500,000
  49. 49. The Strength of ‘Weak’ Ties Does Milgram get it right? (Mark Granovetter) Visualization Source: Early Friendster – MIT Network www.visualcomplexity.com Strong and Weak Ties (Clustered v. Spanning) Clustering ---- My Friends’ Friends are also likely to be friends
  50. 50. So Was Milgram Correct? Small Worlds (i.e. Six Degrees) was a theoretical and an empirical Claim The Theoretical Account Was Incorrect The Empirical Claim was still intact Query as to how could real social networks display both small worlds and clustering? At the Same time, the Strength of Weak Ties was also an Theoretical and Empirical proposition
  51. 51. Watts and Strogatz (1998) A few random links in an otherwise clustered graph yields the types of small world properties found by Milgram “Randomness” is key bridge between the small world result and the clustering that is commonly observed in real social networks
  52. 52. Watts and Strogatz (1998) A Small Amount of Random Rewiring or Something akin to Weak Ties—Allows for Clustering and Small Worlds Random Graphlocally Clustered
  53. 53. Different Form of Network Representation 1 mode 2 mode
  54. 54. Back to the Milgram Experiment
  55. 55. The Milgram Experiment How did the successful subjects actually succeed? How did they manage to get the envelope from nebraska to boston? this is a question regarding how individuals conduct searches in their networks Given most individuals do not know the path to distantly linked individuals
  56. 56. Search in Networks Most individuals do not know the path to an individual who is many hops away Must rely on some sort of heuristic rules to determine the possible path
  57. 57. Search in Networks What information about the problem might the individual attempt to leverage? visual by duncan watts dimensional data: send it to a stockbroker send it to closet possible city to boston
  58. 58. Follow up to the original Experiment available at: http://research.yahoo.com/pub/2397 Published in Science in 2003
  59. 59. 2 mode Actors and Movies Different Forms of Network Representation
  60. 60. 1 mode Actor to Actor Could be Binary (0,1) Did they Co-Appear? Different Forms of Network Representation
  61. 61. Different Forms of Network Representation 1 mode Actor to Actor Could also be Weighted (I.E. Edge Weights by Number of Co-Appearences)
  62. 62. Features of Networks Mesoscopic Community Structures Macroscopic Graph Level Properties Microscopic Node Level Properties
  63. 63. Macroscopic Graph Level Properties Degree Distributions (Outdegree & Indegree) Clustering Coefficients Connected Components Shortest Paths Density
  64. 64. Shortest Paths Shortest Paths The shortest set of links connecting two nodes Also, known as the geodesic path In many graphs, there are multiple shortest paths
  65. 65. Shortest Paths Shortest Paths A and C are connected by 2 shortest paths A – E – B - C A – E – D - C Diameter: the largest geodesic distance in the graph The distance between A and C is the maximum for the graph: 3
  66. 66. Shortest Paths I n t h e W a t t s - S t r o g a t z M o d e l Shortest Paths are reduced by increasing levels of random rewiring
  67. 67. Clustering Coefficients Clustering Coefficients Measure of the tendency of nodes in a graph to cluster Both a graph level average for clustering Also, a local version which is interested in cliqueness of a graph
  68. 68. Density Density = Of the connections that could exist between n nodes directed graph: emax = n*(n-1) (each of the n nodes can connect to (n-1) other nodes) undirected graph emax = n*(n-1)/2
 (since edges are undirected, count each one only once) What Fraction are Present?
  69. 69. Density What fraction are present? density = e / emax For example, out of 12
 possible connections.. this graph this graph has 7, giving it a density of 
 7/12 = 0.58 A “fully connected graph has a density =1
  70. 70. Connected Components We are often interested in whether the graph has a single or multiple connected components Strong Components Giant Component Weak Components
  71. 71. Netlogo Basic Simulation Platform for Agent Based Modeling & Simple Network Simulation http://ccl.northwestern.edu/netlogo/ Wilensky (1999) HIV / VOTING Hawk/Dove (A Classic from Evolutionary Game Theory)
  72. 72. Netlogo Please DownLoad Netlogo as we will be using it occasionally throughout this tutorial http://ccl.northwestern.edu/netlogo/ Wilensky (1999)
  73. 73. Connected Components Open “Giant Component” from the netlogo models Library
  74. 74. Connected Components Notice the fraction of nodes in the giant component Notice the Size of the “Giant Component” Model has been advanced 25+ Ticks
  75. 75. Connected Components Model has been advanced 80+ Ticks Notice the fraction of nodes in the giant component Notice the Size of the “Giant Component”
  76. 76. Connected Components Model has been advanced 120+ Ticks Notice the fraction of nodes in the giant component Notice the Size of the “Giant Component” now = “num-nodes” in the slider
  77. 77. Degree Distributions outdegree
 how many directed edges (arcs) originate at a node indegree
 how many directed edges (arcs) are incident on a node degree (in or out)
 number of edges incident on a node Indegree=3 Outdegree=2 Degree=5
  78. 78. Node Degree from Matrix Values Outdegree: outdegree for node 3 = 2, which we obtain by summing the number of non-zero entries in the 3rd row Indegree: indegree for node 3 = 1, which we obtain by summing the number of non-zero entries in the 3rd column
  79. 79. Degree Distributions These are Degree Count for particular nodes but we are also interested in the distribution of arcs (or edges) across all nodes These Distributions are called “degree distributions” Degree distribution: A frequency count of the occurrence of each degree
  80. 80. Degree Distributions Imagine we have this 8 node network: In-degree sequence: [2, 2, 2, 1, 1, 1, 1, 0] Out-degree sequence: [2, 2, 2, 2, 1, 1, 1, 0] (undirected) degree sequence: [3, 3, 3, 2, 2, 1, 1, 1]
  81. 81. Degree Distributions Imagine we have this 8 node network: In-degree distribution: [(2,3) (1,4) (0,1)] Out-degree distribution: [(2,4) (1,3) (0,1)] (undirected) distribution: [(3,3) (2,2) (1,3)]
  82. 82. Why are Degree Distributions Useful? They are the signature of a dynamic process We will discuss in greater detail tomorrow Consider several canonical network models
  83. 83. Canonical Network Models Erdős-Renyi Random Network Highly Clustered Network Watts-Strogatz Small World Network Barabási-Albert Preferential Attachment Network
  84. 84. Why are Degree Distributions Useful? Barabási-Albert Preferential Attachment Network
  85. 85. Barabási-Albert Preferential Attachment Netlogo Models Library --> Networks --> Preferential Attachment Watch the Changing Degree Distribution
  86. 86. Barabási-Albert Preferential Attachment Netlogo Models Library --> Networks --> Preferential Attachment
  87. 87. Barabási-Albert Preferential Attachment Netlogo Models Library --> Networks --> Preferential Attachment
  88. 88. Barabási-Albert Preferential Attachment Netlogo Models Library --> Networks --> Preferential Attachment
  89. 89. Barabási-Albert Preferential Attachment Netlogo Models Library --> Networks --> Preferential Attachment
  90. 90. Barabási-Albert Preferential Attachment Netlogo Models Library --> Networks --> Preferential Attachment
  91. 91. Readings on Power law / Scale free Networks Check out Lada Adamic’s Power Law Tutorial Describes distinctions between the Zipf, Power-law and Pareto distribution http://www.hpl.hp.com/research/idl/papers/ranking/ranking.html This is the original paper that gave rise to all of the other power law networks papers: A.-L. Barabási & R. Albert, Emergence of scaling in random networks, Science 286, 509–512 (1999)
  92. 92. Power Laws Seem to be Everywhere
  93. 93. Power Laws Seem to be Everywhere
  94. 94. How Do I Know Something is Actually a Power Law?
  95. 95. Clauset, Shalizi & Newman http://arxiv.org/abs/0706.1062 argues for the use of MLE instead of linear regression Demonstrates that a number of prior papers mistakenly called their distribution a power law Here is why you should use Maximum Likelihood Estimation (MLE) instead of linear regression You recover the power law when its present Notice spread between the Yellow and red lines
  96. 96. Back to the Random Graph Models for a Moment Poisson distribution Erdos-Renyi is the default random graph model: randomly draw E edges between N nodes There are no hubs in the network Rather, there exists a narrow distribution of connectivities
  97. 97. Back to the Random Graph Models for a Moment let there be n people p is the probability that any two of them are ‘friends’ Binomial Poisson Normal limit p small Limit large n
  98. 98. Random Graphs Power Law networks
  99. 99. Generating Power Law Distributed Networks Pseudocode for the growing power law networks: Start with small number of nodes add new vertices one by one each new edge connects to an existing vertex in proportion to the number of edges that vertex already displays (i.e. preferentially attach)
  100. 100. Growing Power Law Distributed Networks The previous pseudocode is not a unique solution A variety of other growth dynamics are possible In the simple case this is a system that extremely “sensitive to initial conditions” upstarts who garner early advantage are able to extend their relative advantage in later periods for example, imagine you receive a higher interest rate the more money you have “rich get richer”
  101. 101. Just To Preview The Application to Positive Legal Theory ....
  102. 102. Power Laws Appear to be a Common Feature of Legal Systems Katz, et al (2011) American Legal Academy Katz & Stafford (2010) American Federal Judges Geist (2009) Austrian Supreme Court Smith (2007) U.S. Supreme Court Smith (2007) U.S. Law Reviews Post & Eisen (2000) NY Ct of Appeals
  103. 103. Some Additional Thoughts on the Question...
  104. 104. Back to Network Measures
  105. 105. Node Level Measures Sociologists have long been interested in roles / positions that various nodes occupy with in networks For example various centrality measures have been developed Degree Closeness Here is a non-exhaustive List: Betweenness Hubs/Authorities
  106. 106. Degree Degree is simply a count of the number of arcs (or edges) incident to a node Here the nodes are sized by degree:
  107. 107. Degree as a measure of centrality Please Calculate the “degree” of each of the nodes
  108. 108. Degree as a measure of centrality ask yourself, in which case does “degree” appear to capture the most important actors?
  109. 109. Degree as a measure of centrality what about here, does it capture the “center”?
  110. 110. Closeness Centrality Closeness is based on the inverse of the distance of each actor to every other actor in the network Closeness Formula: Normalized Closeness Formula:
  111. 111. Closeness Centrality
  112. 112. Closeness Centrality
  113. 113. Betweenness Centrality Idea is related to bridges, weak ties This individual may serve an important function Betweenness centrality counts the number of geodesic paths between i & k that actor j resides on
  114. 114. Betweenness Centrality Betweenness centrality counts the number of geodesic paths between i & k that actor j resides on
  115. 115. Betweenness Centrality Check these yourself: gjk = the number of geodesics connecting j & k, and gjk = the number that actor i is on Note: there is also a normalized version of the formula
  116. 116. Betweenness Centrality Betweenness is a very powerful concept We will return when we discuss community detection in networks ... If you want to preview check out this paper: Michelle Girvan & Mark Newman, Community structure in social and biological networks, Proc. Natl. Acad. Sci. USA 99, 7821–7826 (2002) High Betweenness actors need not be actors that score high on other centrality measures (such as degree, etc.) [see picture to the right]
  117. 117. Hubs and Authorities The Hubs and Authorities Algorithm (HITS) was developed by Computer Scientist Jon Kleinberg Similar to the Google “PageRank” Algorithm developed by Larry Page Kleinberg is a MacArthur Fellow and has offered a number of major contributions
  118. 118. Hubs and Authorities We are interested in BOTH: to whom a webpage links and From whom it has received links In Ranking a Webpage ...
  119. 119. Hubs and Authorities Intuition -- If we are trying to rank a webpage having a link from the New York Times is more of than one from a random person’s blog HITS offers a significant improvement over measuring degree as degree treats all connections as equally valuable
  120. 120. Hubs and Authorities Relies upon ideas such as recursion Measure who is important? Measure who is important to who is important? Measure who is important to who is important to who is important ? Etc.
  121. 121. Hubs and Authorities Hubs: Hubs are highly-valued lists for a given query for example, a directory page from a major encyclopedia or paper that links to many different highly-linked pages would typically have a higher hub score than a page that links to relatively few other sources. Authority: Authorities are highly endorsed answers to a query A page that is particularly popular and linked by many different directories will typically have a higher authority score than a page that is unpopular. Note: A Given WebPage could be both a hub and an authority
  122. 122. Hubs and Authorities Hubs and Authorities has been used in a wide number of social science articles There exists some variants of the Original HITS Algorithm Here is the Original Article : Jon Kleinberg, Authoritative sources in a hyperlinked environment, Journal of the Association of Computing Machinery, 46 (5): 604– 632 (1999). Note: there is a 1998 edition as well
  123. 123. Calculating Centrality Measures Thankfully, centrality measures, etc. need not be calculated by hand Lots of software packages ... in increasing levels of difficulty ... left to right Difference in functions, etc. across the packages easy: accepts microsoft excel files Medium: requires the .net / .paj file setup Hard: has lots of features (R or Python)
  124. 124. Daniel Martin Katz Eric Provins! Introduction to Computing for Complex Systems (Session XVII)! Access A Full Step By Step Tutorial for Pajek The Slides From My Intro to Computing for Complex Systems Access Using this Tab
  125. 125. Network Analysis Software Just Download Pajek and Use the Tutorial You should download it to your personal machine MAC Users Note: It is a PC only Program so you will need something like crossover or you will have to multiboot http://pajek.imfm.si/doku.php?id=download
  126. 126. Advanced Network Science Topics Community Detection ERGM Models Diffusion / Social Epidemiology http://computationallegalstudies.com/2009/10/11/ programming-dynamic-models-in-python/
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  170. 170. In Both Citation and Social Networks -- Algorithm Choice Matters
  171. 171. ! MICHAEL!J!BOMMARITO!II!!!!!!!!!DANIEL!MARTIN!KATZ! ! Advanced(Network(Analysis(Methods:( Exponen9al(Random(Graph(Models((p*)( ( #
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  186. 186. http://computationallegalstudies.com/2009/10/11/ programming-dynamic-models-in-python/ Diffusion / Social Epidemiology We Will Discuss An Applied Case Later LaterButIfYouWant to Learn to How To Program the SIR ModelinPython
  187. 187. Network Analysis & Law Mapping Social Structure of Legal Elites (hustle & Flow Article) Diffusion, Norm Adoption and other Related Processes (JLE Article) Legal Doctrine and Legal Rules (Sinks Paper with Application to Patents, etc.)
  188. 188. Example Project #1: Network Analysis of the Social Structure of the the Federal Judiciary
  189. 189. Hustle & Flow: A Social Network Analysis of the American Federal Judiciary Daniel Martin Katz Derek K. Stafford
  190. 190. the Federal Judicial Heirarchy United States Supreme Court Federal Court of Appeals Federal District Court
  191. 191. What is the Social Topology of the American Federal Judiciary?
  192. 192. ... And How Can We Measure it?
  193. 193. Collected Nearly 19,000 Law Clerk ‘Events’ 1995 - 2005 For All Article III Judges Relying Upon Data From Staff Directories Network Analysis of the Federal Judiciary
  194. 194. The Core Claim In the Aggregate ... Law Clerk Movements Reveal Between Judicial Actors Social or Professional Relationships
  195. 195. Network Analysis of the Federal Judiciary Judge E Justice ZJustice Y Judge C Judge D Judge B Judge A
  196. 196. An Sample Line of Dataset
  197. 197. Network Analysis of the Federal Judiciary
  198. 198. Highly Skewed Distribution of Social Authority !
  199. 199. Thirty Most Central Non-SCOTUS Federal Judges (1995-2005) (Eigenvector Centrality) (Eigenvector Centrality) 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 O_Scannlain_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
  200. 200. More Information Here Daniel Katz & Derek Stafford (2010)
  201. 201. Example Project #2: Reproduction of Hierarchy? 
 A Social Network Analysis of the American Law Professoriate
  202. 202. Reproduction of Hierarchy? 
 A Social Network Analysis of the American Law Professoriate Daniel Martin Katz Josh Gubler Jon Zelner Michael Bommarito Eric Provins Eitan Ingall
  203. 203. Motivation for Project Why Do Certain Paradigms, Histories, Ideas Succeed? Function of the ‘Quality’ of the Idea Social Factors also Influence the Spread of Ideas Most Ideas Do Not Persist ....
  204. 204. Law Professors are Important Actors Agents of Socialization Repositories / Distributors of information Socialize Future lawyers, Judges & law Professors Responsible for Developing Particular Legal Ideas (Brandwein (2007) ; Graber (1991), etc.) Law Professor Behavior is a Important Component of Positive Legal Theory Positive Legal Theory
  205. 205. Social Network Analysis Method for Characterizing Diffusion / Info Flow Method for Tracking Social Connections, etc. Method for Ranking Components based upon Various Graph Based Measures
  206. 206. Social Network Analysis of the American Law Professoriate Data Collection
  207. 207. Cornell University Law School
  208. 208. Cornell University Law School
  209. 209. Cornell University Law School
  210. 210. Cornell University Law School
  211. 211. Building A Graph Theoretic Representation Cornell Harvard Penn
  212. 212. Building A Graph Theoretic Representation Cornell Harvard Penn
  213. 213. Building A Graph Theoretic Representation Cornell Harvard Penn
  214. 214. Building A Graph Theoretic Representation Cornell Harvard Penn
  215. 215. Building the Full Dataset
  216. 216. Building the Full Dataset
  217. 217. Building the Full Dataset
  218. 218. Building the Full Dataset
  219. 219. Building the Full Dataset ....
  220. 220. 7,054 Law Professors p = {p1, p2, ... p7240} 184 ABA Accredited Institutions n = {n1 , n2, … n184} Full Data Set ....
  221. 221. Visualizing a Full Network
  222. 222. Visualizing a Full Network Using a Layout Algorithm
  223. 223. Zoomable Visualization Available @ http://computationallegalstudies.com/
  224. 224. Zoomable Visualization Available @ http://computationallegalstudies.com/
  225. 225. A Graph-Based Measure of Centrality
  226. 226. 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...
  227. 227. Hub Score Rank US News Peer Assessment Hub Score Institution 1 1 1 Harvard 2 1 0.9048631 Yale 3 5 0.8511497 Michigan 4 4 0.7952253 Columbia 5 5 0.7737389 Chicago 6 8 0.7026757 NYU 7 1 0.6668868 Stanford 8 8 0.6607399 Berkeley 9 10 0.6457157 Penn 10 10 0.6255498 Georgetown 11 5 0.5854464 Virginia 12 14 0.5014904 Northwestern 13 10 0.4138745 Duke 14 10 0.4075353 Cornell 15 15 0.3977734 Texas 16 28 0.3787268 Wisconsin 17 19 0.3273598 UCLA 18 24 0.2959581 Illinois 19 28 0.2919847 Boston University 20 28 0.2513371 Minnesota 21 24 0.2403289 Iowa 22 28 0.2275534 Indiana 23 19 0.2235015 George Washington24 16 0.2174677 Vanderbilt 25 41 0.2012442 Florida Hub Score Rank US News Peer Assessment 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 0.115086 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 0.103149 Washington & Lee 49 72 0.1027442 Miami 50 103 0.1006172 SUNY Buffalo Hub Scores
  228. 228. 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 0.115086 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 0.103149 Washington & Lee 49 72 0.1027442 Miami 50 103 0.1006172 SUNY Buffalo
  229. 229. 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 0.115086 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 0.103149 Washington & Lee 49 72 0.1027442 Miami 50 103 0.1006172 SUNY Buffalo
  230. 230. 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 0.115086 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 0.103149 Washington & Lee 49 72 0.1027442 Miami 50 103 0.1006172 SUNY Buffalo
  231. 231. 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 0.115086 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 0.103149 Washington & Lee 49 72 0.1027442 Miami 50 103 0.1006172 SUNY Buffalo
  232. 232. 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 0.115086 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 0.103149 Washington & Lee 49 72 0.1027442 Miami 50 103 0.1006172 SUNY Buffalo
  233. 233. 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 0.115086 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 0.103149 Washington & Lee 49 72 0.1027442 Miami 50 103 0.1006172 SUNY Buffalo
  234. 234. Distribution of Social Authority
  235. 235. Top 20 Institutions (By Raw Placements)
  236. 236. 
 

  237. 237. Highly Skewed Nature of Legal Systems Smith 2007 Post & Eisen 2000Katz & Stafford 2010 !
  238. 238. Implications for Rankings Rankings only Imply Ordering ( >, =, < ) End Users tend to Conflate Ranks with Linearized Distances Between Units (Tversky 1977) Non-Stationary Distances Between Entities Both Trivial and Large Distances Linearity Heuristic Often Works Assuming Linearity Can Prove Misleading
  239. 239. Computational Model of Information Diffusion
  240. 240. Why Computational Simulation? History only Provides a Single Model Run Computational Simulation allows ... Consideration of Alternative “States of the world” Evaluation of Counterfactuals
  241. 241. Computational Model of Information Diffusion We Apply a simple Disease Model to Consider the Spread of Ideas, etc. Clear Tradeoff Between Structural Position in the Network and “Idea Infectiousness”
  242. 242. A Basic Description of the Model Consider a Hypothetical Idea Released at a Given Institution Infectiousness Probability = p Two Forms Diffusion... Direct Socialization Signal Giving to Former Students Infect neighbors, neighbors-neighbors, etc.
  243. 243. Lots of Channels of Information Diffusion Among Legal Academics Judicial Decisions, Law Reviews, Other Materials Academic Conferences, Other Professional Orgs SSRN, Legal Blogosphere, etc. Channels of Diffusion Other Channels of Information Dissemination Legal Socialization / Training
  244. 244. A Sample Run of the Model
  245. 245. A Sample Run of the Model
  246. 246. A Sample Run of the Model
  247. 247. A Sample Run of the Model
  248. 248. Run a Simulation on Your Desktop 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/ (Requires Java 5.0 or Higher)
  249. 249. From a Single Run to Consensus Diffusion Plot Netlogo is Good for Model Demonstration Regular Programming Language Typically Required for Full Scale Implementation We Used Python http://ccl.northwestern.edu/netlogo/ http://www.python.org/ Object Oriented Programming Language
  250. 250. From a Single Run to Consensus Diffusion Plot Repeated the Diffusion Simulation Hundreds of Model Runs Per School Yielded a Consensus Plot for Each School Results for Five Emblematic Schools Exponential, linear and sub-linear
  251. 251. 
 Computational Simulation of Diffusion upon the Structure of the American Legal Academy
  252. 252. Differential Host Susceptibility Some Potential Model Improvements? Countervailing Information / Paradigms S I R Model Susceptible-Infected-Recovered
  253. 253. Directions for Future Research Longitudinal Data Hiring/Placement/Laterals Current Collecting Data Database Linkage to Articles/Citations Working with Content Providers Empirical Evaluation of Simulation Computational Lingusitics Text Mining, Sentiment Coding
  254. 254. Example Project #3: On the Road to the Legal Genome Project ... Dynamic Community Detection & Distance Measures for Dynamic Citation Networks
  255. 255. Distance Measures for Dynamic Citation Networks Michael J. Bommarito II Daniel Martin Katz Jon Zelner James H. Fowler
  256. 256. Imagine
  257. 257. Ideas
  258. 258. Represented as Colors
  259. 259. How Can We Track the Novel Combination, Mutation and Spread of Ideas?
  260. 260. Information Genome Project The Development, Mutation and and Spread of Ideas Precedent in Common Law Systems Patent Citations Bibliometric Analysis
  261. 261. Citations Represent the Fossil Record
  262. 262. They are the Byproduct of Dynamic Processes
  263. 263. Information Genomics
  264. 264. Leverging the Ideas in Network Community Detection
  265. 265. Want to Develop a Method that can Identify the Time Dependant ...
  266. 266. Changing Relationships between Various Intellectual Concepts
  267. 267. (1)Patent Citations (2) Judicial Decisions (3) Academic Articles
  268. 268. Applied Traditional Methods to SCOTUS Citation Network
  269. 269. Applied Traditional Methods to SCOTUS Citation Network #EPICFAIL
  270. 270. Here is Proof of the #EPICFAIL
  271. 271. Reported the Results at ASNA 2009
  272. 272. Key Points from the ASNA 2009 Paper
  273. 273. Key Points from the ASNA 2009 Paper
  274. 274. Key Points from the ASNA 2009 Paper
  275. 275. We Decided to Go Back to First Principles
  276. 276. Growth Rules For Citation Networks
  277. 277. Dynamic Directed Acyclic Graphs
  278. 278. Dynamic Directed Acyclic Graphs Examples: Academic Articles
  279. 279. Dynamic Directed Acyclic Graphs Examples: Academic Articles Judicial Citations
  280. 280. Dynamic Directed Acyclic Graphs Examples: Academic Articles Judicial Citations Patent Citations
  281. 281. Network Dynamics: The Early Jurisprudence of the United States Supreme Court
  282. 282. Cases Decided by the Supreme Court Citations in the Current Year Citations from prior years PLAY MOVIE! http://computationallegalstudies.com/ 2010/02/11/the-development-of-structure-in- the-citation-network-of-the-united-states- supreme-court-now-in-hd/
  283. 283. A Formalization of D-DAG’s
  284. 284. Six Degrees of Marbury v. Madison
  285. 285. A Formalization of D-DAG’s
  286. 286. Basic Idea of Sink Based Distance Measure
  287. 287. The Simplest Non-Trivial Distance Measure
  288. 288. Flexible Framework For More Detailed Specifications
  289. 289. Distance Measure <- -> Dendrogram
  290. 290. http://ssrn.com/author=627779 http://arxiv.org/abs/0909.1819available at:
  291. 291. Expect More in Judicial Citation Dynamics ....
  292. 292. Here is Another Application ...
  293. 293. Potential Application to Patent Citations?
  294. 294. Sternitzke, Bartkowski & Schramm (2008) Potential Application to Patent Citations?
  295. 295. Network Analysis of Patent Citations
  296. 296. Network Analysis of Patent Citations
  297. 297. http://www.eecs.umich.edu/cse/dm_11_video/erdi.mp4 http://people.kzoo.edu/~perdi/Talk By Péter Érdi Network Analysis of Patent Citations
  298. 298. Some Papers For Your Consideration
  299. 299. Click Here to Access
  300. 300. @computational Thank You For Your Attention!

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