The Web of Law

Scientists and mathematicians in recent years have become intensely interested in the structure of networks. Networks turn out to be crucial to understanding everything from physics and biology, to economics and sociology. This article proposes that the science of networks has important contributions to make to the study of law as well. The network of American case law closely resembles the Web in structure and can be studied using techniques that are now being used to describe many other networks, some found in nature, and others created by human action. Studying the legal network can shed light on how the legal system evolves, and many other questions. I present in this article the preliminary results of a significant citation study of nearly four million American legal precedents, which was undertaken at my request by the LexisNexis corporation using the Shepard's citation service. This study demonstrates that the American case law network has the overall structure that network theory predicts it would. It is a highly skewed, scale-free, or similar network. The remarkably great degree of skew is significant. Precendential authority is concentrated in a small number of cases. The vast majority of cases are rarely or never cited. In that it consists largely of dead cases, the Web of Law closely resembles scientific paper citation networks, which consist mostly of dead papers. This article has three parts. First, I introduce some basic concepts of network science, including such important ideas as nodes, links, random graphs, evolving networks, scale-free networks, small worlds, the rich get richer dynamic, node fitness, and clusters. In Part II, I show that both over all and by particular jurisdiction, the Web of Law is a scale-free or similarly highly skewed network. In Part III, I describe some insights that appear from this application and suggest areas for future research. The Web of Law has a structure very similar to that of other real networks, such as the Web and the network of scientific papers. Indeed, preliminary analysis suggests the citation network of U.S. Supreme Court cases is nearly identical to the network of high-energy physics papers, and is well described by a two-power-law model. The Web of Law is organized with hub cases that have many citations and the vast majority of cases, which have very few. The distribution of citation frequency appears to be well described by a two power-law distribution, very similar to scientific paper citation networks. Many promising hypotheses can be generated by considering the law as a scale-free network. State and federal systems can be examined empirically to measure how well integrated each is with itself, and with each other, and how this is changing over time. Legal authorities can be measured to determine whether their authority is emerging or declining. Institutional bodies, such as courts, can be examined in the same way. Clusters of cases, which will reveal the semantic topology of law, can be mapped to determine whether traditional legal categories are accurate or require reform. These methods can be used to develop computer programs to improve the efficiency of searching electronic legal databases. Network theory hints at complex, but analyzable, interactions between the legal doctrines of precedent, and the systems of common law and multiple sovereignties. Because law grows and because it has doctrines of authority, it creates a network of a certain shape, which spontaneously organizes itself. Legal databases, which are huge, precisely documented, and readily accessible, present a perfect opportunity for the application of network science. This research would produce new knowledge of general jurisprudence that has simply been impossible until now, when we have the necessary advances in network science, the fast computers, and the existence of a complete record of the legal network in electronic form, waiting to be explored.