Legal hypergraphs.

Complexity science provides a powerful framework for understanding physical, biological and social systems, and network analysis is one of its principal tools. Since many complex systems exhibit multilateral interactions that change over time, in recent years, network scientists have become increasingly interested in modelling and measuring dynamic networks featuring higher-order relations. At the same time, while network analysis has been more widely adopted to investigate the structure and evolution of law as a complex system, the utility of dynamic higher-order networks in the legal domain has remained largely unexplored. Setting out to change this, we introduce temporal hypergraphs as a powerful tool for studying legal network data. Temporal hypergraphs generalize static graphs by (i) allowing any number of nodes to participate in an edge and (ii) permitting nodes or edges to be added, modified or deleted. We describe models and methods to explore legal hypergraphs that evolve over time and elucidate their benefits through case studies on legal citation and collaboration networks that change over a period of more than 70 years. Our work demonstrates the potential of dynamic higher-order networks for studying complex legal systems, and it facilitates further advances in legal network analysis. This article is part of the theme issue 'A complexity science approach to law and governance'.

GPT-4 passes the bar exam.

In this paper, we experimentally evaluate the zero-shot performance of GPT-4 against prior generations of GPT on the entire uniform bar examination (UBE), including not only the multiple-choice multistate bar examination (MBE), but also the open-ended multistate essay exam (MEE) and multistate performance test (MPT) components. On the MBE, GPT-4 significantly outperforms both human test-takers and prior models, demonstrating a 26% increase over ChatGPT and beating humans in five of seven subject areas. On the MEE and MPT, which have not previously been evaluated by scholars, GPT-4 scores an average of 4.2/6.0 when compared with much lower scores for ChatGPT. Graded across the UBE components, in the manner in which a human test-taker would be, GPT-4 scores approximately 297 points, significantly in excess of the passing threshold for all UBE jurisdictions. These findings document not just the rapid and remarkable advance of large language model performance generally, but also the potential for such models to support the delivery of legal services in society. This article is part of the theme issue 'A complexity science approach to law and governance'.

Complex societies and the growth of the law.

While many informal factors influence how people interact, modern societies rely upon law as a primary mechanism to formally control human behaviour. How legal rules impact societal development depends on the interplay between two types of actors: the people who create the rules and the people to which the rules potentially apply. We hypothesise that an increasingly diverse and interconnected society might create increasingly diverse and interconnected rules, and assert that legal networks provide a useful lens through which to observe the interaction between law and society. To evaluate these propositions, we present a novel and generalizable model of statutory materials as multidimensional, time-evolving document networks. Applying this model to the federal legislation of the United States and Germany, we find impressive expansion in the size and complexity of laws over the past two and a half decades. We investigate the sources of this development using methods from network science and natural language processing. To allow for cross-country comparisons over time, based on the explicit cross-references between legal rules, we algorithmically reorganise the legislative materials of the United States and Germany into cluster families that reflect legal topics. This reorganisation reveals that the main driver behind the growth of the law in both jurisdictions is the expansion of the welfare state, backed by an expansion of the tax state. Hence, our findings highlight the power of document network analysis for understanding the evolution of law and its relationship with society.

A general approach for predicting the behavior of the Supreme Court of the United States.

Building on developments in machine learning and prior work in the science of judicial prediction, we construct a model designed to predict the behavior of the Supreme Court of the United States in a generalized, out-of-sample context. To do so, we develop a time-evolving random forest classifier that leverages unique feature engineering to predict more than 240,000 justice votes and 28,000 cases outcomes over nearly two centuries (1816-2015). Using only data available prior to decision, our model outperforms null (baseline) models at both the justice and case level under both parametric and non-parametric tests. Over nearly two centuries, we achieve 70.2% accuracy at the case outcome level and 71.9% at the justice vote level. More recently, over the past century, we outperform an in-sample optimized null model by nearly 5%. Our performance is consistent with, and improves on the general level of prediction demonstrated by prior work; however, our model is distinctive because it can be applied out-of-sample to the entire past and future of the Court, not a single term. Our results represent an important advance for the science of quantitative legal prediction and portend a range of other potential applications.