Computational Legal Studies™

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.

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) and Holz (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 a hierarchical 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.

Click on the above picture and you will be taken to the Interactive Gallery of Computational Legal Studies. Once inside the gallery, click on any thumbnail to see the full size image. Each image features a link to supporting materials such as documentation and/or the underlying academic paper. We hope to add more content to gallery over the coming weeks and months — so please check back!  Please note that load time may vary depending upon your connection, machine, etc.

Tomorrow is the first day of presentations at NetSci2010. Our paper will presented in AM Network Measures Panel.  Anyway, for those interested in leveraging network science to study the dynamics of large social and physical systems — the conference promises a fantastic lineup of speakers. Check out the program!

Thanks to Carl Malamud and the good folks at the University of Colorado Law School and University of Texas Law School for allowing us to participate in their respective law.gov meetings. For those interested in governmental transparency, we believe that Carl Malamud’s on-going national conversation is very important. The video above represents a fixed spaced movie combining the majority of the slides we presented at the two meetings. If the video will not load, click here to access the YouTube Version of the Slides. Enjoy!

The above image is a visualization of temporal citation patterns in the history of the United States Supreme Court.  Each case is placed horizontally across the image in chronological order.  We then draw citations between cases as curved arcs.  We use three distinct arc colors to show qualitative differences between these citations:

• RED arcs correspond to citations within a natural court (e.g., the Rehnquist court citing the Rehnquist court).
• GREEN arcs correspond to citations from one natural court to the previous natural court (e.g., the Rehnquist court citing the Burger court).
• BLUE arcs correspond to citations from one natural court to a natural court prior to the previous natural court (e.g., the the Rehnquist court citing the Marshall court).
• Note that yellow is produced when red and green overlap.

Though there are many ways to interpret this data, we wanted to provide three simple conclusions to draw:

1. The number of cases decided within each natural court varies dramatically.  For instance, the Rehnquist court decided fewer cases than the Fuller court.
2. Most citations are to recent cases, not cases in the distant past.
3. The Burger and Rehnquist courts rely heavily on cases from the Hughes, Stone, and Vinson courts

Tommorow is the Law.gov meeting at Texas Law School where Mike and I will be presenting in the afternoon session.  We are looking forward to the discussion!  Thanks to Terry Martin and Carl Malamud for organizing the event.  For those interested, click on the image above and you will be directed to the agenda for the meeting.

The visualization above is something we call “six degrees” of Marbury v. Madison.  It was originally produced for use in our paper Distance Measures for Dynamic Citation Networks. Due to space considerations, we ended up leaving it on the cutting room floor.  However, the visual is designed to highlight the idea of a “sink.”

Sinks are one of the core concepts which we outline in our Distance Measures for Dynamic Citation Networks paper.  Looking through the prism of a citation network, sinks are the root to which a given legal concept, academic idea or patent based innovation can be drawn. From each citation in a non-sink node, it is possible to trace the chains of citations back to their root (which we call a sink).  In the visualization above, the root or sink node is the famed United States Supreme Court decision Marbury v. Madison.  Starting from the center and working out to the edge, the first ring are cases that directly cite Marbury v. Madison.  The next ring are cases which cite cases that cite Marbury v. Madison.  The next ring are cases which cite cases which cases that cite Marbury v. Madison and so on…

Anyway, one of the major contributions of the Distance Measures for Dynamic Citation Networks paper is that it allows us to use these sinks to create pairwise distance/similarity measure between the ith and jth unit. In this instance, the units in this directed acyclic network are the ith and jth decisions of the United States Supreme Court.

Now, it is important to note cases contain many citations and thus can be oriented relative to many different sinks.  So, even if a case can be traced to the Marbury sink – this does not preclude it from being traced to other sinks as well.  Also, it is possible to design many mathematical functions to characterize the sink based distance between units. For instance, the importance of a sink might decay as its shortest path length increases. An alternative measure might weight the importance of each sinks by the number of unique ancestors shared between nodes i and j that are descended from a given sink of interest. Indeed, many fine-grained choices are possible but they require justification drawn from the given substantive problem …