A pioneering research project applying computational methods to measure and analyze the complexity of the United States Code, demonstrating how legal complexity can be quantified using mathematical and network science approaches.

Research Overview

This project develops an empirical framework for measuring legal complexity by representing the U.S. Code as a mathematical object with multiple dimensions including hierarchical structure, citation networks, and linguistic content.

Publication

Authors: Daniel Martin Katz, Michael James Bommarito
Published: Artificial Intelligence and Law, Volume 22 (2014)
Paper: Available on SSRN
Initial Release: August 1, 2013

Methodology

The research introduces a novel multi-dimensional approach to legal complexity:

1. Mathematical Representation

U.S. Code modeled as a multinetwork/multilayered network
Hierarchical structure analysis
Citation network mapping
Content-based topic modeling

2. Complexity Metrics

Shannon Entropy for information complexity
Network centrality measures
Linguistic complexity indicators
Composite scoring across dimensions

3. Data Sources

Cornell Legal Information Institute
Complete U.S. Code corpus (22+ million words)
Cross-reference and citation data

Key Findings

The analysis reveals:

Legal complexity “taxes cognition and increases the likelihood of suboptimal decisions”
Significant variation in complexity across different U.S. Code titles
Correlation between regulatory domain complexity and legal text complexity
Quantifiable patterns in legal structure evolution

Technical Implementation

The project includes:

Python scripts for text processing and analysis
Network analysis algorithms
Data visualization tools
Reproducible research framework

Impact

This research pioneered computational legal studies by:

Establishing quantitative methods for legal complexity measurement
Providing empirical basis for legal reform discussions
Demonstrating applications of complexity science to law
Creating reusable frameworks for legal text analysis

Led to subsequent publications including:

“A Mathematical Approach to the Study of the United States Code” (Physica A, 2010)
“Harnessing Legal Complexity” with J.B. Ruhl (Science Magazine, 2017)