A Mathematical Approach to the Study of the United States Code

TL;DR

This paper formalizes a mathematical model of the United States Code as a hierarchical and citation network, enabling measurement of its structural and linguistic changes over time.

Contribution

It introduces a novel formalization of the Code as a combined hierarchical and citation network, facilitating quantitative analysis of its evolution.

Findings

The Code increased in structural complexity over time.

Interdependence among provisions grew in recent years.

The language used in the Code expanded and became more intricate.

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.