Measuring the Complexity of the Law : The United States Code

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.

Court Under Roberts Is Most Conservative in Decades [Via NY Times]

The Sunday New York Times features an article by Adam Liptak assessing the conservatism of Robert Court.  The article features some good coverage for some of the leading law and political science scholars who study the United States Supreme Court.  Well worth the read!

Oklahoma's Infamous Ballot Initiative – State Question 755 [Via the Economist]

In addition to my interests related to the theme of this blog, I have a number of ongoing projects related to American direct democracy. Thus, I will be following with interest the recent developments in Oklahoma. According to the Economist, “… Rex Duncan, a Republican member of Oklahoma’s House of Representatives has just had a measure placed on the November ballot that would ban local courts from considering sharia, or Islamic law, in their judgments.” Proponents of the measure have dubbed it the “Save our State” amendment. State Question Number 755 will ask voters to amend Section 1 of Article VII of the state Constitution to require the state courts to rely only on federal and state law when deciding cases. It forbids courts from considering or using Sharia law.

Suffice to say, the Economist was less than impressed with actions of the Oklahoma Legislature.  Indeed, I have reviewed virtually every ballot initiative across every State for the past thirty years and would say even in the demagoguery laden world of American direct democracy that this represents some sort of a low point.

Iowa Electronic Markets: Who Will Win Control of the House in the 2010 Midterms?

For many years, the Iowa Electronic Markets have served as a futures market for political and economic information.  As we move to the fall, the race for control of the House (and in turn the Speakership) appears to hang in the balance.  The plot above offers both the current spot price as well as historic information regarding the markets’ perspective on this important race. Click here for information regarding this specific market.

Irrelevant Events Affect Voters’ Evaluations of Government Performance [PNAS]

In PNAS this week Andrew J. Healy, Neil Malhotra, and Cecilia Hyunjung Mo offer Irrelevant Events Affect Voters’ Evaluations of Government Performance.  From the abstract:  “Does information irrelevant to government performance affect voting behavior? If so, how does this help us understand the mechanisms underlying voters’ retrospective assessments of candidates’ performance in office? To precisely test for the effects of irrelevant information, we explore the electoral impact of local college football games just before an election, irrelevant events that government has nothing to do with and for which no government response would be expected. We find that a win in the 10 days before Election Day causes the incumbent to receive an additional 1.61 percentage points of the vote in Senate, gubernatorial, and presidential elections, with the effect being larger for teams with stronger fan support. In addition to conducting placebo tests based on postelection games, we demonstrate these effects by using the betting market’s estimate of a team’s probability of winning the game before it occurs to isolate the surprise component of game outcomes. We corroborate these aggregate-level results with a survey that we conducted during the 2009 NCAA men’s college basketball tournament, where we find that surprising wins and losses affect presidential approval. An experiment embedded within the survey also indicates that personal well-being may influence voting decisions on a subconscious level. We find that making people more aware of the reasons for their current state of mind reduces the effect that irrelevant events have on their opinions. These findings underscore the subtle power of irrelevant events in shaping important real-world decisions and suggest ways in which decision making can be improved.”