Computational Legal Studies™

What are some of the key takeaway points?

(1) The Supreme Court’s increasing reliance upon its own decisions over the 1800-1830 window.

(2) The important role of maritime/admiralty law in the early years of the Supreme Court’s citation network. At least with respect to the Supreme Court’s citation network, these maritime decisions are the root of the Supreme Court’s jurisprudence.

(3) The increasing centrality of decisions such as Marbury v. Madison, Martin v. Hunter’s Lessee to the overall network.

The Development of Structure in the SCOTUS Citation Network

The visualization offered above is the largest weakly connected component of the citation network of the United States Supreme Court (1800-1829). Each time slice visualizes the aggregate network as of the year in question.

In our paper entitled Distance Measures for Dynamic Citation Networks, we offer some thoughts on the early SCOTUS citation network. In reviewing the visual above note ….“[T]he Court’s early citation practices indicate a general absence of references to its own prior decisions. While the court did invoke well-established legal concepts, those concepts were often originally developed in alternative domains or jurisdictions. At some level, the lack of self-reference and corresponding reliance upon external sources is not terribly surprising. Namely, there often did not exist a set of established Supreme Court precedents for the class of disputes which reached the high court. Thus, it was necessary for the jurisprudence of the United States Supreme Court, seen through the prism of its case-to-case citation network, to transition through a loading phase. During this loading phase, the largest weakly connected component of the graph generally lacked any meaningful clustering. However, this sparsely connected graph would soon give way, and by the early 1820’s, the largest weakly connected component displayed detectable structure.”

What are the elements of the network?

What are the labels?

To help orient the end-user, the visualization highlights several important decisions of the United States Supreme Court offered within the relevant time period:

Marbury v. Madison, 5 U.S. 137 (1803) we labeled as ”Marbury”
Murray v. The Charming Betsey, 6 U.S. 64 (1804) we labeled as “Charming Betsey”
Martin v. Hunter’s Lessee, 14 U.S. 304 (1816) we labeled as “Martin’s Lessee”
The Anna Maria, 15 U.S. 327 (1817) we labeled as “Anna Maria”
McCulloch v. Maryland, 17 U.S. 316 (1819) we labeled as “McCulloch”

Why do cases not always enter the visualization when they are decided?

As we are interested in the core set of cases, we are only visualizing the largest weakly connected component of the United States Supreme Court citation network. Cases are not added until they are linked to the LWCC. For example, Marbury v. Madison is not added to the visualization until a few years after it is decided.

How do I best view the visualization?

Given this is a high-definition video, it may take few seconds to load. We believe that it is worth the wait. In our view, the video is best consumed (1) Full Screen (2) HD On (3) Scaling Off.

Where can I find related papers?

Here is a non-exhaustive list of related scholarship:

Michael Bommarito, Daniel Katz, Jon Zelner & James Fowler, Distance Measures for Dynamic Citation Networks, Physica A __ (2010 Forthcoming).

Yonatan Lupu & James Fowler, The Strategic Content Model of Supreme Court Opinion Writing, APSA 2009 Toronto Meeting Paper.

Michael Bommarito, Daniel Katz & Jon Zelner, Law as a Seamless Web? Comparison of Various Network Representations of the United States Supreme Court Corpus (1791-2005) in Proceedings of the 12th Intl. Conference on Artificial Intelligence and Law (2009).

Frank Cross, Thomas Smith & Antonio Tomarchio, The Reagan Revolution in the Network of Law, 57 Emory L. J. 1227 (2008).

James Fowler & Sangick Jeon, The Authority of Supreme Court Precedent, 30 Soc. Networks 16 (2008).

Elizabeth Leicht, Gavin Clarkson, Kerby Shedden & Mark Newman, Large-Scale Structure of Time Evolving Citation Networks, 59 European Physics Journal B 75 (2007).

Thomas Smith, The Web of the Law, 44 San Diego L.R. 309 (2007).

James Fowler, Timothy R. Johnson, James F. Spriggs II, Sangick Jeon & Paul J. Wahlbeck, Network Analysis and the Law: Measuring the Legal Importance of Precedents at the U.S. Supreme Court, 15 Political Analysis, 324 (2007).
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With nine weeks to go before the 2010 Midterm Elections, it is worth checking in with Iowa Electronic Markets to see where things stand. “The IEM 2010 Congressional Election Markets are real-money futures markets where contract payoffs will be determined by the votes cast in the 2010 U.S. Congressional Elections. “Congress10” (plotted above) is based on the composition of both houses of Congress.”

Take a look at the plot above. You will notice there has been significant movement in the past few weeks. Consistent with the beliefs of a number of pundits, the dominant scenario for 2010 is split control “RH_DS10″ (i.e Republican House and Democrat Senate). Whether you view this outcome as good or bad, it is important to emphasize there is still time left and these trends could reverse.

[HT: Paul Kedrosky & Tim O'Riley ]

What is the World Treaty Index?

The World Treaty Index (WTI), originally compiled by Peter Rohn in the 1960s and 1970s and subsequently maintained and updated at the University of Washington, is a comprehensive list of all known treaties formed during the twentieth century.  This includes not only treaties formally registered with the United Nations (UNTS) but a significant number of unregistered agreements.

What information does the World Treaty Index provide?

The WTI provides information on the parties to the agreement, the general topic of the agreement (e.g. trade agreement, tax agreement, an arms control agreement, etc.), as well as the signing date and the date in force, and the volume and page containing the text of the agreement.  Though the WTI does not provide the full text of each agreement, it is an excellent resource for identifying when a state (or states) formed a number of international agreements of a particular type.  With a list of relevant agreements (including their volume and page number), an end user interested in obtaining the full text can simply collect them using the primary source material (i.e. UNTS, LTS, etc.)

Who is currently administrating the World Treaty Index?

The Electronic WTI is now housed at the University of Michigan and administrated by Michael Bommarito, Daniel Martin Katz and Paul Poast. We are highlighting the newly constructed Beta Prerelease of the WTI website in an effort to obtain feedback prior to the official release. The currently available product provides access to information on more than 50,000 bilateral and multilateral treaties formed between 1945 and 1997. When full coverage for the 20th century is complete, the database should feature in excess of 80,000 agreements.

What are some examples of searches I can conduct on the World Treaty Index website?

While the WTI should support all browsers, we suggest using Firefox.  Below are three sample searches.

Search #1: Suppose a user would like to collect all agreements involving Brazil. Use the “flexible search” and follow three easy steps.  (A) Select the country/organization field  (B) within the country/organization field set the field value = Brazil  (C) click the search button.

Search #2: Suppose a user would like to collect all agreements between Mexico and Spain. Use the “flexible search” and follow five easy steps.  (A) Select the country/organization field  (B) within the country/organization field set the field value = Mexico (C) Select a second country/organization field (B) within this new country/organization field set the field value = Spain  (E) now click the search button.

Search #3: Suppose a user would like to know how many extradition agreements France signed between 1950 and 1962.  This is similar to the examples above but involves the topic, signed on or after and signed before or on fields. After the user chooses the proper search fields and selects the search information, the WTI will produce on the screen a list of the desired agreements and provide the option of downloading the list as a CSV file.

When will it feature full coverage for the entire 20th Century?

By the end of 2010, we will add (1) all treaties formed between 1900 and 1944, (2) all treaties formed between 1998 and 1999, and (3) a list of all parties to a given multilateral agreement.  If you know of an agreement that is not ultimately featured on the site please contact us and we will be happy to add it to the list.

How can I learn more about the World Treaty Index?

For a general history of the World Treaty Index, visit the “History Page” on the worldtreatyindex.com website.  For a more detailed treatment please see: Glenda Pearson, Rohn’s World Treaty Index: Its Past and Future, 29 International Journal of Legal Information 543 (2001).

What additional extensions of the Electronic World Treaty Index are planned?

As noted above, our initial goal is provide complete coverage of all known agreements in the 20th Century. Planned extensions include bringing the World Treaty forward so as to provide coverage up to 2010.  In addition, we plan to collect information regarding treaty terminations. Finally, we would like to enhance the granularity of our topic codes and allow for agreements with multiple dimensions to feature multiple topic codes.

This week’s issue of the Economist has an interesting article entitled Riders on a Swarm. Among other things, the article discusses how attempts to computationally model ant, bee and bird behavior have offered insight into major problems in artificial intelligence.

For those not familiar, the examples discussed within the article are classic models in the science of complex systems. For example, here is the Netlogo implementation of bird flocking. It will run in your browser but requires Java 4.1 or higher. If you decide to take a look — please click setup – then go to make the model run. Once inside the Netlogo GUI, you can explore how various parameter configurations impact the model’s outcomes.

One of the major insights of the bird flocking model is how random starting conditions and local behavioral rules can lead to the emergence of observed behavioral patterns that appear (at least on first glance) to be orchestrated by some sort of top down command structure.

This is, of course, not the case. The model is bottom up and not top down. Both the simplicity and the bottom up flavor of the model are apparent when you explore the model’s code. For those interested, I will take a second and plug the slides from my ICPSR class. In the class, I dedicated about an hour of class time to bird flocking model. Click here for the slides. In the slides, I walk through some of the important features of the code (discussion starts on slide 16).

Understanding the sources of complexity in legal systems is a matter long considered by legal commentators. In tackling the question, scholars have applied various approaches including descriptive, theoretical and, in some cases, empirical analysis. The list is long but would certainly include work such as Long & Swingen (1987), Schuck (1992), White (1992), Kaplow (1995), Epstein (1997), Kades (1997), Wright (2000), Holz (2007) and Bourcier & Mazzega (2007). Notwithstanding the significant contributions made by these and other scholars, we argue that an extensive empirical inquiry into the complexity of the law still remains to be undertaken.

While certainly just a slice of the broader legal universe, the United States Code represents a substantively important body of law familiar to both legal scholars and laypersons. In published form, the Code spans many volumes. Those volumes feature hundreds of thousands of provisions and tens of millions of words. The United States Code is obviously complicated, however, measuring its size and complexity has proven be non-trivial.

In our paper entitled, A Mathematical Approach to the Study of the United States Code we hope to contribute to the effort by formalizing the United States Code as a mathematical object with ahierarchical structure, a citation network and an associated text function that projects language onto specific vertices.

In the visualization above, Figure (a) is the full United States Code visualized to the section level. In other words, each ring is a layer of a hierarchical tree that halts at the section level. Of course, many sections feature a variety of nested sub-sections, etc. For example, the well known 26 U.S.C. 501(c)(3) is only shown above at the depth of Section 501.  If we added all of these layers there would simply be additional rings. For those interested in the visualization of specific Titles of the United States Code … we have previously created fully zoomable visualizations of Title 17 (Copyright), Title 11 (Bankruptcy), Title 26 (Tax) [at section depth], Title 26 (Tax) [Capital Gains & Losses] as well as specific pieces of legislation such as the original Health Care Bill – HR 3962.

In the visualization above, Figure (b) combines this hierarchical structure together with a citation network.  We have previously visualized the United States Code citation network and have a working paper entitled Properties of the United States Code Citation Network. Figure (b) is thus a realization of the full United States Code through the section level.

With this representation in place, it is possible to measure the size of the Code using its various structural features such as vertices V and its edges E.  It is possible to measure the full Code at various time snapshots and consider whether the Code is growing or shrinking. Using a limited window of data, we observe growth not only in the size of the code but also its network of dependancies (i.e. its citation network).

Of course, growth in the size United States Code alone is not necessarily analogous to an increase in complexity.  Indeed, while we believe in general the size of the code tends to contribute to “complexity,” some additional measures are needed.  Thus, our paper features structural measurements such as number of sections, section sizes, etc.

In addition, we apply the well known Shannon Entropy measure (borrowed from Information Theory) to evaluate the “complexity” of the message passing / language contained therein. Shannon Entropy has a long intellectual history and has been used as a measure of complexity by many scholars.  Here is the formula for Shannon entropy:

For those interested in reviewing the full paper, it is forthcoming in Physica A: Statistical Mechanics and its Applications. For those not familiar, Physica A is a journal published by Elsevier and is a popular outlet for Econophysics and Quantitative Finance. A current draft of the paper is available on the SSRN and the physics arXiv.

We are currently working on a follow up paper that is longer, more detailed and designed for a general audience.  Even if you have little or no interest in the analysis of the United States Code, we hope principles such as entropy, structure, etc. will prove useful in the measurement of other classes of legal documents including contracts, treaties, administrative regulations, etc.