Computational Legal Studies™

Together with Derek Stafford from the University of Michigan Department of Political Science, Hustle and Flow: A Social Network Analysis of the American Federal Judiciary represents our initial foray into Computational Legal Studies. The full paper contains a number of interesting visualizations where we draw various federal judges together on the basis of their shared law clerks (1995-2004). The screen print above is a zoom very center of the center of the network.  Yellow Nodes represent Supreme Court Justices, Green Nodes represent Circuit Court Justices, Blue Nodes represent District Court Justices.

There exist many high quality formal models of judicial decision making including those considering decisions rendered by judges in judicial hierarchy, whistle blowing, etc. One component which might meaningfully contribute to the extent literature is the rigorous consideration of the social and professional relationships between jurists and the impacts (if any) these relationships impose upon outcomes. Indeed, from a modeling standpoint, we believe the “judicial game” is a game on a graph–one where an individual strategic jurist must take stock of time evolving social topology upon which he or she is operating. Even among judges of equal institutional rank, we observe jurists with widely variant levels social authority (specifically social authority follows a power law distribution).

So what does all of this mean? Take whistle blowing — the power law distribution implies that if the average judge has a whistle, the “super-judges” we identify within the paper could be said to have an air horn. With the goal of enriching positive political theory / formal modeling of the courts, we believe the development of a positive theory of judicial social structure can enrich our understanding of the dynamics of prestige and influence. In addition, we believe, at least in part, “judicial peer effects” can help legal doctrine socially spread across the network. In that vein, here is a view of our operationalization of the social landscape … a wide shot of the broader network visualized using the Kamada-Kawai visualization algorithm:

Here is the current abstract for the paper: Scholars have long asserted that social structure is an important feature of a variety of societal institutions. As part of a larger effort to develop a fully integrated model of judicial decision making, we argue that social structure-operationalized as the professional and social connections between judicial actors-partially directs outcomes in the hierarchical federal judiciary. Since different social structures impose dissimilar consequences upon outputs, the precursor to evaluating the doctrinal consequences that a given social structure imposes is a descriptive effort to characterize its properties. Given the difficulty associated with obtaining appropriate data for federal judges, it is necessary to rely upon a proxy measure to paint a picture of the social landscape. In the aggregate, we believe the flow of law clerks reflects a reasonable proxy for social and professional linkages between jurists. Having collected available information for all federal judicial law clerks employed by an Article III judge during the “natural” Rehnquist Court (1995-2004), we use these roughly 19,000 clerk events to craft a series of network based visualizations.   Using network analysis, our visualizations and subsequent analytics provide insight into the path of peer effects in the federal judiciary. For example, we find the distribution of “degrees” is highly skewed implying the social structure is dictated by a small number of socially prominent actors. Using a variety of centrality measures, we identify these socially prominent jurists. Next, we draw from the extant complexity literature and offer a possible generative process responsible for producing such inequality in social authority. While the complete adjudication of a generative process is beyond the scope of this article, our results contribute to a growing literature documenting the highly-skewed distribution of authority across the common law and its constitutive institutions.

dmartink Uncategorized Judicial Decision Making, Judicial Peer Effects, Law as a Complex System, network analysis, Public Law, supreme court

Several months ago, I put together this syllabus for use in a hypothetical seminar course entitled Law as a Complex System. I hoped to revise this reading list / syllabus and have now done so …. While this revised version might contain more content than would be practical for the typical 2-3 credit seminar, I do believe it is far more reasonable than Version 1.0. For anyone who is interested in learning more about the methodological tradition from which much of our scholarship is drawn … feel free to use this as a reading list. If you see any law related scholarship you believe should be included please feel free to email me.

dmartink Uncategorized computational social science, Law as a Complex System

Do legal systems have physical properties? Considered in the aggregate, do the distinctions upon distinctions developed by common law judges self-organize in a manner that can be said to have definable physical property (at least at the broad level of abstraction)? The answer might lie in fractal geometry.

Fractal geometry was developed in a set of classic papers by mathematician Benoît Mandelbrot. The original paper in the field How Long is the Coastline of Britain describes the coastline measurement problem.  In short form, the length of the coast line is a function of the size of measurement one employs.  As shown below, as the unit of measurement decreases the length of the coastline increases.  The ideas expressed in this and subsequent papers have been applied to a wide class of substantive questions. In particular, the application to economic systems has been particularly illuminating. Given recent economic events, we agree with views of the Everyday Economist arguing the applied economic theory built upon his work should earn Mandelbrot a share of the Nobel Prize.

A more abstract fractal is the simple version of the Sierpinski triangle displayed at the top of this post. Here, there exists self similarity at all levels. Specifically, at each iteration of the model, the triangles at the tip of each of the lines replicate into self similar versions of the original triangle. If you click on the visual above, you can run the applet (provided you have java installed on your computer). {Side note: those of you NKS Wolfram fans out there will know the Sierpinski triangle can be generated using cellular automata Rule 90.}

For those who are interested in another demonstration consider the Koch Snowflake — a fractal which also offers a view of the relevant properties.  The Koch Snowflake is a curve with infinite length (i.e. there is no convergence even though it is located in a bounded region around the original triangle).  Click here to view an online demo of the Koch Snowflake.

So, you might be wondering … what is the law analog to fractals? As a first-order description of one important dynamic of the common law, we believe significant progress can be made by considering the conditions under which legal systems behave in a manner similar to fractals. For those interested, a number of important papers have discussed the fractal nature of legal systems.  While discussing legal argumentation, the original idea is outlined in two important early papers The Crystalline Structure of Legal Thought and  The Promise of Legal Semiotics both by Jack Balkin.  The empirical case begins in work such as How Long is the Coastline of the Law? Thoughts on the Fractal Nature of Legal Systems by David G. Post & Michael B. Eisen and continues in more recent work such as The Web of the Law by Thomas Smith.

In our view, the utility of this research is not to adjudicate the common law to be a fractal.  Indeed, there exist mechanisms which likely prevent legal systems from actually behaving as unbounded fractal.  The purpose of the discussion is determine whether describing law as a fractal is a reasonable first-order description of at least one dynamic within this complex adaptive system. While full adjudication of these questions is still an area of active research, we highlight these ideas for their important potential contribution to positive legal theory.

One thing we want to flag is the important relationship between the power law distributions we discussed in these prior posts (here and here) and the original work of  Benoît Mandelbrot.  The mapping of the power law like properties displayed by the common law and its constitutive institutions is part of the larger empirical case for the fractal nature of legal systems. Building upon the prior work, in two recent papers, which are available on SSRN here and here, we mapped this property of self organization among two sets of legal elites — judges and law professors.

dmartink Uncategorized classic models, evolution of law, Law as a Complex System

As we mentioned in previous posts, Seadragon is a really cool product. Please note load times may vary depending upon your specific machine configuration as well as the strength of your internet connection. For those not familiar with how to operate it please see below. In our view, the Full Screen is best the way to go ….

dmartink Uncategorized computational linguistics, judicial citation network, Law as a Complex System, supreme court

For the third installment of posts related to Reproduction of Hierarchy? A Social Network Analysis of the American Law Professoriate, we offer a Netlogo simulation of intellectual diffusion on the network we previously visualized.  As noted in prior posts, we are interested legal socialization and its role in considering the spread of particular intellectual or doctrinal paradigms. This model captures a discrete run of the social epidemiological model we offer in the paper.   As we noted within the paper, this represents a first cut on the question—where we favor parsimony over complexity.  In reality, there obviously exist far more dynamics than we engage herein.  The purpose of this exercise is simply to begin to engage the question. In our estimation, a positive theory of law should engage the sociology of the academy — a group who collectively socialize nearly every lawyer and judge in the United States. In the paper and in the model documentation, we offer some possible model extensions which could be considered in future scholarship.

Once you click through to the model, here is how it works:

(1) Click the Setup Button in the Upper Left Corner.  This will Display the Network in the Circular Layout.

(2) Click the Layout Button.  Depending upon the speed of your machine this may take up to 30 seconds.  Stop the Layout Button by Re-Clicking the Button.

(3) Click the Size Nodes by Degree Button. You Will Notice the Fairly Central Node Colored in Red.  This is School #12 Northwestern University Law School.  Observe how we have set the default infected school as #12 Northwestern (Hat Tip to Uri Wilensky).  A Full List of School Number is available at the bottom of the page when you click through.

(4) Now, we are ready to begin.  Click the Spread Once Button.  The idea then reaches its neighbors with probability p (set as a default at .05).  You can click the Toggle Infection Tree button (at any point) to observe the discrete paths traversed by the idea.

(5) Click the Spread Once Button, again and again.  Notice the plot tracking the time on the x axisand the number of institution infected on the y axis.  This is an estimate of the diffusion curve for the institution.

(6) To restart the simulation, click the Reinfect One button.  Prior to hitting this button, slide theInfected Slider to any Law School you would like to observe.  Also, feel free to adjust the p slider to increase or decrease the infectiousness of the idea.

Please comment if you have any difficulty or questions.  Note you must have Java 1.4.1 + installed on your computer.  The Information Technology professionals at many institutions will have already installed this on your machine but if not you will need to download it.   We hope you enjoy!

dmartink Uncategorized agent based models, Law as a Complex System, network analysis, social epidemiology

As was stated in Part 1 of this thread, it is by no means a given that the statistical artifact displayed above would appear. Namely, such large scale patterns need not assume this flavor as many social and physical systems feature substantially different properties.

For purpose of generating an empirically grounded theory of American Common Law development … explaining these artifacts would seem to critical. Fortunately, with respect to the above pattern, there exist a definable set of generative processes plausibly responsible for producing what is displayed. While certainly not the only generative process responsible for a power law, the preferential attachment model, first outlined in the physics literature by Barabási & Albert, is among the likely candidates.

Confronting much of the extant literature, query as to whether a closed form equilibria based analytical apparatus (punctuated or otherwise) is up to the task of describing the relevant dynamics? If anything, the distributions displayed above provide first-order evidence of a system which is likely to feature dynamics of a non-linear flavor. Indeed, while significant work still remains, the weight of available evidence indicates Law is a Complex Adaptive System. As such, we believe it would be appropriate to leverage the methods typically reserved for the study of complexity.  For purposes of generating positive legal theory, we believe agent based models, dynamic network analysis and other methods of computational social science offer great potential. We encourage scholars to consider learning more about these approaches.

dmartink Uncategorized computational legal studies, evolution of law, judicial citation network, Judicial Peer Effects, Law as a Complex System

Anton Geist has posted Using Citation Analysis Techniques for Computer-Assisted Legal Research in Continental Jurisdictions to the SSRN.  While this is certainly longer than most papers, we believe it offers a good review of the broader information retrieval and law literature.  In addition, it offers some empirical insight into citation patterns within continental jurisdictions. The findings in this paper are similar to those shown in important papers by Thomas Smith in The Web of the Law and by David Post & Michael Eisen in How Long is the Coastline of Law? Thoughts on the Fractal Nature of Legal Systems. 

In our view, the next step for this research is to determine whether the pattern does indeed follow a power law distribution.  Specifically, there exists a Maximum Likelihood based test developed in the applied physics paper Power-law Distributions in Empirical Data by Aaron Clauset, Cosma Shalizi and Mark Newman which can help adjudicate whether the detected pattern represents a highly skewed distribution or is indeed a power law.

Either way, we are excited by this paper as we believe comparative research is absolutely critical to broader theory development.

dmartink Uncategorized algorithms, computational legal studies, judicial citation network, Judicial Decision Making, Law as a Complex System

In our paper Law as a Seamless Web, we offer a first-order method to generate case-to-case and opinionunit-to-opinionunit semantic networks. As constructed in the figure above, nodes represent cases decided between 1791-1865 while edges are drawn when two cases possess a certain threshold of semantic similarity. Except for the definition of edges, the process of constructing the semantic graph is identical to that of the citation graph we offered in the prior post. While computer science/computational linguistics offers a variety of possible semantic similarity measures, we choose to employ a commonly used measure. Here a description from the paper:

“Semantic similarity measures are the focus of significant work in computational linguistics. Given the scope of the dataset, we have chosen a first-order method for calculating similarity.  After lemmatizing the text of the case with WordNet, we store the nouns with the top N frequencies for each case or opinion unit. We define the similarity between two cases or opinion units A and B as the percentage of words that are shared between the top words of A and top words of B.

An edge exists between A and B in the set of edges  if  σ (A,B) exceeds some threshold.  This threshold is the minimum similarity necessary for the graph to represent the presence of a semantic connection.”  

As this a technical paper, it is slanted toward demonstrating proof of methodological concept rather than covering significant substantive ground. With that said, we do offer a hint of our broader substantive goal of detecting the spread of legal concepts between various topical domains. Specifically, with respect to enriching positive political theory, we believe union, intersect and compliment of the semantic and citation networks are really important. More on this point is forthcoming in a subsequent post…

dmartink Uncategorized computational linguistics, evolution of law, judicial citation network, Law as a Complex System, network analysis

Several months ago, I put together this syllabus for use in a future seminar course Law as a Complex System. This contains far more content than would be practical for the typical 2 credit seminar. However, I have decided to repost this because it could also serve as a reading list for anyone who is interested in learning more about the methodological tradition from which must of our scholarship is drawn. If you see any law related scholarship you believe should be included please feel free to email me.

dmartink Uncategorized evolution of law, Law as a Complex System

We have recently posted Law as a Seamless Web? Comparison of Various Network Representations of the United States Supreme Court Corpus (1791-2005) to the SSRN. Given this is the first of several posts about the paper, I will speak broadly and leave details for a subsequent post. From the abstract “As research of judicial citation and semantic networks transitions from a strict focus on the structural characteristics of these networks to the evolutionary dynamics behind their growth, it becomes even more important to develop theoretically coherent and empirically grounded ideas about the nature of edges and nodes. In this paper, we move in this direction on several fronts …. Specifically, nodes represent whole cases or individual ‘opinion units’ within cases. Edges represent either citations or semantic connections.” The table below outlines several possible network representations for the USSC corpus. 

The goal of the paper is to do some technical and conceptual work. It is a small slice of broader project with James Fowler (UCSD) and James Spriggs (WashU). We recently presented findings from the primary project at the Networks in Political Science Conference. The main project is entitled The Development of Community Structure in the Supreme Court’s Network of Citations and we hope to have a version of this paper on the SSRN soon. In the meantime, we plan additional discussion of Law as a Seamless Web in the days to come.  

dmartink Uncategorized computational linguistics, computational social science, evolution of law, judicial citation, Law as a Complex System, network analysis, supreme court