Network Analysis and the Law
Daniel Martin KatzMichigan State University
College of Law
Michael J. Bommarito IICenter for Study of
Complex Systems
Jurix 2011 Tutorial @ Universität Wien
!
My Background
Assistant Professor of LawMichigan State University
Former NSF IGERT Fellow,University of Michigan
Center for the Study of Complex Systems(2009-2010)
PhDPolitical Science & Public Policy
University of Michigan(2011)
JDUniversity of Michigan
Law School(2005)
My Background
Former NSF IGERT Fellow,University of Michigan
Center for the Study of Complex Systems
PhD Pre-CandidateDept. of Political Science
University of Michigan
Masters DegreeFinancial EngineeringUniversity of Michigan
Blog:
Daniel Martin Katz(Michigan State
University - College of Law)
Michael Bommarito II
(Michigan Complex Systems)
JonZelner
(PrincetonEcology & Evolutionary
Biology)
PrimaryContact
Information
http://www.law.msu.edu/faculty_staff/profile.php?
prof=780
http://computationallegalstudies.com/
Outline of Our Session
Network Analysis: An Extended Primer
Network Analysis & Law
The Frontier of Network Analysis & Law
Legal ElitesDiffusion and other Related ProcessesLegal Doctrine and Legal Rules
Advanced Network Science Topics Community Detection ERGM / P* ModelsSocial Epidemiology
Distance Measures for Dynamic Citation NetworksDynamic Community DetectionThe Judicial Collaborative Filter (Judge Aided Info Retrevial)
Network Analysis: An Extended Primer
Introduction to Network Analysis
What is a Network?
What is a Social Network?
Mathematical Representation of theRelationships Between Units such asActors, Institutions, Software, etc.
Special class of graph Involving Particular Units and Connections
Introduction to Network Analysis
Interdisciplinary Enterprise
Applied Math(Graph Theory, Matrix Algebra, etc.)
Statistical Methods
Social Science
Physical and Biological Sciences
Computer Science
Social Science
For Images and Links to Underlying projects:
http://jhfowler.ucsd.edu/
3D HiDef SCOTUS Movie
Co-Sponsorship in CongressSpread of Obesity
Hiring and Placement of Political Science PhD’s
Social Science
The 2004 Political Blogosphere (Adamic & Glance)
High School Friendship(Moody)
Roll Call Votes in United States Congress(Mucha, et al)
Physical and Biological Sciences
For Images and Links to Underlying projects:
http://www.visualcomplexity.com/vc/
Computer Science
Mapping
of the
Code
Networks are waysto represent dependanciesbetween software
Computer Science
Internet is one ofthe largest
known and most important networks
Computer Science
Mappingthe
Iranian Blogsphere
http://cyber.law.harvard.edu/publications/2008/Mapping_Irans_Online_Public
Primer on Network
Terminology
Terminology & Examples
Institutions
Firms
States/Countries
Actors
NODES
Other
Example: Nodes in an actor- based social Network
Alice
Bill
Carrie
David
Ellen
How Can We Represent The Relevant Social Relationships?
Terminology & Examples
Edges
Alice
Bill
Carrie
David
Ellen
Arcs
Terminology & Examples
Edges
Alice Bill
Carrie
David
Ellen
Arcs
Terminology & Examples
Edges Alice BillCarrie
David
Ellen
Arcs
Terminology & Examples
Alice Bill
David
Carrie
Ellen
A Full Representation of the Social Network
Terminology & Examples
Bill
David
Carrie
Ellen
Terminology & Examples
Alice
A Full Representation of the Social Network(With Node Weighting)
Bill
David
Carrie
Ellen
A Full Representation of the Social Network(With Node Weighting and Edge Weighting)
Terminology & Examples
Alice
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
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 21 31 41 52 12 33 43 53 25 15 45 35 2
ROWS è COLUMNS
*How to Read the Edge List: (Person in Column 1 is friends with Person in Column 2)
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
A Quick Law Based Example of a
Dynamic Network
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/
Some Other Examples
of Networks
Consumer Data
Knowing Consumer Co-Purchases can help ensure that “Loss Leader” Discounts can be recouped with other purchases
Transportation Networks
We might be interested in developing transportation systems that are minimize
total travel time per passenger
Power Grids
We might be interested in developing Power Systems that are Globally Robust to Local Failure
Campaign Contributions Networks
http://computationallegalstudies.com/tag/110th-congress/
The United States Code
http://computationallegalstudies.com/
+
Hierarchical Structure
Some Recent Network Related
Publications
Special Issue: Complex systems
and NetworksJuly 24, 2009
Special 90th anniversary Issue:
May 7, 2007
History ofNetwork Science
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?
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?
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 pointcan have 0 or 2 nodes with an odd degree
Hamiltonian path: visiteach vertex exactly once
ModernNetwork Science
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
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?
Stanley Milgram’s Other Experiment
NE
MA
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”
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/
Six Degrees of Kevin Bacon
Visualization Source: Duncan J. Watts, Six Degrees
Six Degrees of Kevin Bacon
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
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
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
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
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
Different Form of Network Representation
1 mode
2 mode
Back to the Milgram
Experiment
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
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
Search in Networks
What information about the problem might the individual attempt to leverage?
visual by duncan watts
dimensional data:
send it to a stockbrokersend it to closet possible city to boston
Follow up to the original Experiment
available at: http://research.yahoo.com/pub/2397
Published in Science in 2003
2 mode
Actors and
Movies
Different Forms of Network Representation
1 mode
Actor to Actor
Could be Binary (0,1)
Did they Co-Appear?
Different Forms of Network Representation
Different Forms of Network Representation
1 mode
Actor to Actor
Could also beWeighted
(I.E. Edge Weights by Number of
Co-Appearences)
Features of Networks
Mesoscopic Community Structures
Macroscopic Graph Level Properties
Microscopic Node Level Properties
Macroscopic Graph Level Properties
Degree Distributions (Outdegree & Indegree)
Clustering Coefficients
Connected Components
Shortest Paths
Density
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
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
Shortest Paths
In the Watts -Strogatz Model Shortest Paths are reduced by increasing levels of random rewiring
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
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?
DensityWhat fraction are present?density = e / emax
For example, out of 12possible connections.. this graph
this graph has 7, giving it a density of 7/12 = 0.58
A “fully connected graph has a density =1
Connected Components
We are often interested in whether the graph has a single or multiple connected components
Strong Components
Giant Component
Weak Components
NetlogoBasic 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)
Netlogo
Please DownLoad Netlogo as we will be using it occasionally
throughout this tutorial
http://ccl.northwestern.edu/netlogo/
Wilensky (1999)
Connected Components
Open “Giant Component” from the netlogo models Library
Connected Components
Notice the fraction of nodes in the
giant component
Notice the Size of the “Giant
Component”
Model has been
advanced 25+ Ticks
Connected Components
Model has been
advanced 80+ Ticks
Notice the fraction of nodes in the
giant component
Notice the Size of the “Giant
Component”
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
Degree Distributions
outdegreehow many directed edges (arcs) originate at a node
indegreehow 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
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
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
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]
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)]
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
Canonical Network Models
Erdős-Renyi Random Network
Highly Clustered Network
Watts-Strogatz Small World Network
Highly Clustered Highly Clustered
Barabási-Albert Preferential
Attachment Network
Why are Degree Distributions Useful?
Barabási-Albert Preferential
Attachment Network
Barabási-Albert Preferential Attachment
Netlogo Models Library --> Networks --> Preferential Attachment
Watch the Changing Degree Distribution
Barabási-Albert Preferential Attachment
Netlogo Models Library --> Networks --> Preferential Attachment
Barabási-Albert Preferential Attachment
Netlogo Models Library --> Networks --> Preferential Attachment
Barabási-Albert Preferential Attachment
Netlogo Models Library --> Networks --> Preferential Attachment
Barabási-Albert Preferential Attachment
Netlogo Models Library --> Networks --> Preferential Attachment
Barabási-Albert Preferential Attachment
Netlogo Models Library --> Networks --> Preferential Attachment
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)
Power Laws Seem to be Everywhere
Power Laws Seem to be Everywhere
How Do I Know Something is Actually a Power Law?
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
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
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
Random Graphs
Power Law networks
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)
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”
Just To Preview The Application to Positive
Legal Theory ....
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
Smith (2007)U.S. Law Reviews
Some Additional Thoughts on the Question...
Back to Network Measures
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
DegreeDegree is simply a count of the number of arcs (or edges) incident to a node
Here the nodes are sized by degree:
Degree as a measure of centrality
Please Calculate the “degree” of each of the nodes
Degree as a measure of centrality
ask yourself, in which case does “degree” appear to capture the most important actors?
Degree as a measure of centrality
what about here, does it capture the “center”?
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:
Closeness Centrality
Closeness Centrality
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
Betweenness Centrality
Betweenness centrality counts the number of geodesic paths between i & k that actor j resides on
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
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]
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
Hubs and Authorities
We are interested in BOTH:
to whom a webpage links
and
From whom it has received links
In Ranking a Webpage ...
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
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.
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
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
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: acceptsmicrosoft excel files
Medium: requires the .net / .paj
file setup
Hard: has lots of features
(R or Python)
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
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
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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http://computationallegalstudies.com/2009/10/11/programming-dynamic-models-in-python/
Diffusion / Social Epidemiology
We Will Discuss An Applied Case Later Later But If You Want to Learn to How To Program the SIR Model in Python
BREAK FOR 15 Minutes
We Will Next Move Into Applied Network Analysis
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.)
Example Project #1:
Network Analysis of the Social Structure of the
the Federal Judiciary
Hustle & Flow: A Social Network Analysis of the American
Federal Judiciary
Daniel Martin Katz Derek K. Stafford
the Federal Judicial Heirarchy
United States Supreme Court
Federal Court of Appeals
Federal District Court
What is the Social Topology of the American Federal Judiciary?
... And How Can We Measure it?
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
The Core Claim
In the Aggregate ...
Law Clerk Movements Reveal
Between Judicial Actors
Social or Professional Relationships
Network Analysis of the Federal Judiciary
Judge E
Justice ZJustice Y
Judge C
Judge D
Judge BJudge A
An Sample Line of Dataset
Network Analysis of the Federal Judiciary
Highly Skewed Distribution of Social
Authority
!
Thirty Most Central
Non-SCOTUSFederal Judges
(1995-2005)
(Eigenvector Centrality)
Thirty Most Central Federal Judges (1995-2004)
(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
More Information Here
Daniel Katz & Derek Stafford
(2010)
Example Project #2:
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?
Function of the ‘Quality’ of the Idea
Social Factors also Influence the Spread of Ideas
Most Ideas Do Not Persist ....
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
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
Social Network Analysis of the American Law Professoriate
Data Collection
Cornell University Law School
Cornell University Law School
Cornell University Law School
Cornell University Law School
Building A Graph Theoretic Representation
Cornell
Harvard Penn
Building A Graph Theoretic Representation
Cornell
Harvard Penn
Building A Graph Theoretic Representation
Cornell
Harvard Penn
Building A Graph Theoretic Representation
Cornell
Harvard Penn
Building the Full Dataset
Building the Full Dataset
Building the Full Dataset
Building the Full Dataset
Building the Full Dataset
....
7,054 Law Professors! p = {p1, p2, ... p7240}
184 ABA Accredited Institutions n = {n1 , n2, … n184}
Full Data Set
....
Visualizing a Full Network
Visualizing a Full NetworkUsing a Layout Algorithm
Zoomable Visualization Available @ http://computationallegalstudies.com/
Zoomable Visualization Available @ http://computationallegalstudies.com/
A Graph-Based Measure of Centrality
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
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 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
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
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 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
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
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 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
37 82 0.1232289 Rutgers Camden38 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
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 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
37 82 0.1232289 Rutgers Camden38 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 Howard44 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
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 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
37 82 0.1232289 Rutgers Camden38 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 Howard44 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
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
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)
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
Computational Simulation allows ... Consideration of Alternative “States of the world”
Evaluation of Counterfactuals
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”
A Basic Description of the Model
Consider a Hypothetical Idea Released at a Given Institution
Infectiousness Probability = p
Two Forms Diffusion...Direct SocializationSignal Giving to Former Students
Infect neighbors, neighbors-neighbors, etc.
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
A Sample Run of the Model
A Sample Run of the Model
A Sample Run of the Model
A Sample Run of the Model
Run a Simulationon 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)
From a Single Run to Consensus Diffusion Plot
Netlogo is Good for Model Demonstration
Regular Programming Language TypicallyRequired for Full Scale Implementation
We Used Python
http://ccl.northwestern.edu/netlogo/
http://www.python.org/
Object Oriented Programming Language
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 SchoolsExponential, linear and sub-linear
!
Computational Simulation of Diffusion upon the Structure of the American Legal Academy
Differential Host Susceptibility
Some Potential Model Improvements?
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
Empirical Evaluation of SimulationComputational LingusiticsText Mining, Sentiment Coding
Example Project #3:
On the Road to the Legal Genome Project ...
Dynamic Community Detection
&
Distance Measures for Dynamic Citation Networks
Distance Measures for Dynamic Citation Networks
Michael J. Bommarito IIDaniel Martin Katz
Jon Zelner James H. Fowler
Imagine
Ideas
Represented as Colors
How Can We Track the Novel
Combination, Mutation and
Spread of Ideas?
Information Genome Project
The Development, Mutation and and Spread of Ideas
Precedent in Common Law Systems
Patent Citations
Bibliometric Analysis
Citations Represent the Fossil Record
They are the Byproduct of
Dynamic Processes
Information Genomics
Leverging the Ideas in Network
Community Detection
Want to Develop a Method that can Identify the Time
Dependant ...
Changing Relationships
between Various Intellectual
Concepts
(1)Patent Citations
(2) Judicial Decisions
(3) Academic Articles
Applied Traditional Methods to SCOTUS Citation Network
Applied Traditional Methods to SCOTUS Citation Network
#EPICFAIL
Here is Proof of the #EPICFAIL
Reported the Results at ASNA 2009
Key Points from the ASNA 2009 Paper
Key Points from the ASNA 2009 Paper
Key Points from the ASNA 2009 Paper
We Decided to Go Back to First
Principles
Growth Rules For Citation Networks
Dynamic Directed Acyclic Graphs
Dynamic Directed Acyclic Graphs
Examples: Academic Articles
Dynamic Directed Acyclic Graphs
Examples: Academic Articles
Judicial Citations
Dynamic Directed Acyclic Graphs
Examples:
Academic Articles
Judicial Citations
Patent Citations
Network Dynamics:
The Early Jurisprudence of the United States Supreme Court
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/
A Formalization of D-DAG’s
Six Degrees of Marbury v. Madison
A Formalization of D-DAG’s
Basic Idea of Sink Based Distance Measure
The Simplest Non-Trivial Distance Measure
Flexible Framework For More Detailed Specifications
Distance Measure <- ->
Dendrogram
http://ssrn.com/author=627779
http://arxiv.org/abs/0909.1819available at:
Expect More in Judicial Citation
Dynamics ....
Here is Another Application ...
Potential Application to Patent Citations?
Sternitzke, Bartkowski & Schramm (2008)
Potential Application to Patent Citations?
Network Analysis of Patent Citations
Network Analysis of Patent Citations
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
Some Papers
For Your
Consideration
Click Here to
Access
@computational
Thank You For Your Attention!
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