A Mathematical Approach to the Study of the United States Code

A Mathematical Approach to the Study of the United States Code Michael J. Bommarito II Center for the Study of Complex Systems, University of Michigan, Ann Arbor Department of Political Science, University of Michigan, Ann Arbor Department of Financial Engineering, University of Michigan, Ann Arbor Daniel M. Katz Center for the Study of Complex Systems, University of Michigan, Ann Arbor Department of Political Science, University of Michigan, Ann Arbor University of Michigan Law School Abstract The United States Code (Code) is a document containing over 22 million words that represents a large and important source of Federal statutory law. Scholars and policy advocates often discuss the direction and magnitude of changes in various aspects of the Code. However, few have mathematically formalized the notions behind these discussions or directly measured the resulting representations. This paper addresses the current state of the literature in two ways. First, we formalize a representation of the United States Code as the union of a hierarchical network and a citation network over vertices containing the language of the Code. This representation reflects the fact that the Code is a hierarchically organized document containing language and explicit citations between provisions. Second, we use this formalization to measure aspects of the Code as codified in October 2008, November 2009, and March 2010. These measurements allow for a characterization of the actual changes in the Code over time. Our findings indicate that in the recent past, the Code has grown in its amount of structure, interdependence, and language. Keywords: United States Code, hierarchical network, citation network, language, computational legal studies 1. Formalizing the Code The United States Code (Code) is a document con- taining over 22 million words that represents a large and important source of Federal statutory law. The Code is a concise and conveniently organized compilation of all rati- fied legislation and treaties, and is often the first source of information for lawyers, judges, and legal academics.1 The Code is compiled through a process known as codification, which is carried out by the Office of the Law Revision Counsel (LRC), an organization within the U.S. House of Representatives. The LRC’s goal in this codification process is to transform the incremental and chronological Statutes at Large into the Code, a current snapshot of the law that is organized into hierarchical categories.2 Email addresses: mjbommar@umich.edu (Michael J. Bommarito II), dmartink@umich.edu (Daniel M. Katz) 1The complete set of all ratified legislation and treaties is known as the Statutes at Large. As a legal technicality, the Code is only prima facie evidence of Federal law. In the event of a discrepancy, the Statutes at Large are the final authority. Furthermore, additional sources such as the Code of Federal Regulations contains clarifica- tions issued by other Federal agencies or bodies. 22 U.S.C. §285- §285g outlines the purpose, policy and functions of the Office of Law Revision Counsel. This hierarchical organization is an important quali- tative feature of the Code. At the first level of the hi- erarchy, the Code is divided into 49 titles that represent the broadest categories of law. Well-known titles include the Tax Code, formally known as Title 26 - Internal Rev- enue Code, Title 20 - Education, and Title 18 - Crimes and Criminal Punishment. Each title is also hierarchi- cally subdivided into some combination of subtitles, chap- ters, subchapters, parts, subparts, sections, subsections, paragraphs, subparagraphs, clauses, or subclauses. Out of these vertex types, only sections, subsections, paragraphs, subparagraphs, clauses and subclauses can contain the ac- tual substantive legal text. The text within these vertices can also contain explicit citations to other portions of the Code. These citations may be used to reference definitions, highlight qualifying conditions, or point to well-understood processes. It is critical to recognize that these citations are not restricted by the organizational hierarchy. For example, sections within Title 26, the Tax Code, can and do contain ci- tations to Title 18, the Criminal Code. Thus, though the LRC attempts to organize the Code into a cleanly divided hierarchical network, there is also a citation network em- Preprint submitted to Elsevier October 22, 2018 arXiv:1003.4146v1 [cs.IR] 22 Mar 2010 bedded within the Code that is not constrained by this hierarchy. Based on the characterization above, we can formulate a mathematical representation of the Code as a graph G = (V, E) with an associated “text” function T(v). V is the set of vertices composed of all titles, subtitles, chapters, subchapters, parts, subparts, sections, subsections, para- graphs, subparagraphs, clauses, and subclauses. These vertices can also be divided into two subsets: (1) vertices that do contain text, written V T , and (2) vertices that do

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