• CFRED CUHK Law

Measuring Law Over Time

Corinna Coupette, Max Planck Institute for Informatics;

Janis Beckedorf, Ruprecht-Karls-Universität Heidelberg;

Dirk Hartung, Center for Legal Technology and Data Science;

Michael Bommarito, CodeX – The Stanford Center for Legal Informatics;

Daniel Martin Katz, Chicago-Kent College of Law


-- Modern products and services easily concern a large variety of legal questions and, consequently, are affected by a plethora of legal rules. These rules are themselves interdependent, and they influence each other in legally relevant ways. In an increasingly digitized world, this ever-growing amount of interconnected information can make it hard for lawyers to cut through the noise and find relevant answers to their clients’ legal needs. Clients, in turn, might wonder which regulatory areas are investment-friendly, how to monitor regulatory change, or simply whether they should hire an additional employee for their legal department.


To answer these questions realistically, we need to understand how legal systems evolve in this day and age. To this end, it does not suffice to learn whether the amount of regulation in a legal system decreases or increases. We also ought to know when, where, how ,and—ideally—why. We must investigate which legal domains drive the changes we observe, and ask whether our traditional understanding of clearly distinguishable areas of law still holds in an increasingly interconnected world. And we have to analyze the importance of individual legal rules, along with their function in the regulatory environment and the systemic consequences of changing them. In a nutshell: We need to develop the tools to measure, monitor, and manage legal complexity in the era of global digitalization.


Our paper, Measuring Law Over Time, takes a step towards this goal. Drawing on concepts and methods from complexity science and network analysis, we propose a framework for modeling legal documents as multi-dimensional, dynamic document networks. The entities in these networks are (substructures of) legal documents (possibly in different countries or at different points in time), and the relationships between the entities encode references (e.g., one section of a statute citing another section) or hierarchical inclusion (e.g., a chapter of a regulation containing several subchapters). Since networks have underlying mathematical representations, called graphs, that lend themselves to systematic algorithmic analysis, modeling legal documents as networks allows us to leverage computer science tools for studying the law. Consequently, we propose a catalog of methods designed to reveal novel insights into the law at all scales: from the context and evolution of individual legal rules (micro level) via the organization of areas of law (meso level) to invariants of legal systems (macro level).


We demonstrate the utility of our framework by applying it to an original dataset of statutes and regulations from two different countries, the United States and Germany, spanning more than twenty years (1998–2019). On the macro level, we find, inter alia, that both the United States legal system and the German legal system at the federal level have experienced significant growth over the past decades, but while codified law in the United States has become increasingly dominated by regulations, codified law in Germany remains governed by statutes. On the meso level, we show that legal system growth in both countries can be attributed to particular areas of law, which we identify using a data-driven approach that exploits the references between legal rules, rather than an externally imposed taxonomy. On the micro level, we classify individual legal rules based on their navigational function, identifying certain patterns of local reference connectivity as signatures of peculiar, country-specific drafting styles. Finally, in a case study on financial regulation, we generate statistical profiles for prominent laws in the domain, charting legal evolution much like stock market trends.


Our application highlights the potential of network analysis that is truly tailored to the legal domain. Therefore, we hope that the conceptual and methodological framework we propose encourages legal scholars, computer scientists, and social physicists to join our quest toward building a complete toolkit for measuring, monitoring, and managing legal complexity. Our most recent work, which builds on our previous study published in Scientific Reports, is published with open access in Frontiers in Physics; a preprint version is also available on SSRN. We welcome any feedback via email to dirk.hartung@law-school.de.

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