The premise of a new Special Issue of the Philosophical Transactions of the Royal Society A (Mathematical, Physical and Engineering Sciences), published past month is that legal systems are complex adaptive systems, and thus complexity science can be usefully applied to improve understanding of how legal systems operate, perform and change over time.

Legal systems are social systems—they are composed of networks of institutions (courts, legislatures, agencies) and instruments (laws, regulations, judicial decisions)—and thus it is not surprising that complexity science also included legal systems within its scope. Indeed, in his influential work forging the earliest frameworks of complexity science, Kauffmann posited that common law judicial systems are CAS.

In fairness to the sceptics, and in contrast to its progress in other social sciences, most of the work framing legal systems as CAS in these descriptive and prescriptive phases was non-empirical. The turning point in this regard came in the late 2000s as legal and policy scholars began applying computational tools, in particular from network science, to explore legal system components and behaviour.

With publication of this stream of work in prominent peer-reviewed journals, the proposition that legal systems are CAS gained increasing adoption and by 2020 had achieved a substantial degree of acceptance within the mainstream scientific community

The application of complexity science to study legal systems is now producing a richly diverse and robust body of research.

In the introduction¹ by Pierpaolo Vivo, Daniel M. Katz and J. B. Ruhl there is a comprehensive summary of the articles. Very interestingly, at least 5 of them focus on the use/ application of current LLM IA models to legal practices (highlighted below):

Legal systems

• Lee & Cantwell [36] develop a minimal model of judicial decision-making that takes into account the judges’ individual bias as well as peer interactions in a Court.
• In Coupette et al. higher-order network interactions—and their time evolution—are considered for the first time in the legal context.
• Soh develops a novel automated pipeline for discovering significant topics from legal decision texts.

Legal institutions

• Mastrandrea et al. apply complex networks methods and tools to analyse the coalitions formed by EU nations and institutions during litigation proceedings at the European Court of Justice over the period 1977–2018.
• Adipudi & Kim develop a conceptual framework for analysing international institutions as complex systems.
• Herron et al. use a dynamic influence model to examine the role of the US Supreme Court in influencing the direction of legal discourse in the lower federal courts.
• Ash et al. explore the potential relationship between legal code complexity and population size in US localities. In other words, does the complexity of a municipal code scale with the size of a given city?

Legal practice and context

• Nay et al. test the legal analysis abilities of Large Language Models (LLMs) (from smaller and weaker models up to the state-of-the-art, notably OpenAI’s GPT-4) in applying US tax law.
• Goodenough & Carlson observe that as the complexity of society has increased, so has the complexity of law, to a point where we are pushing the effective limits of traditional systems of word-based legal rules.
• Sichelman & Smith construct a basic toy model of real property relations, and define (and measure) the level of ‘legal modularity’ of the corresponding network model.
• Gray et al. consider the question to what extent GPT Family Models could assist human annotators in identifying legally relevant factors in a given case. They focus on DIAS (Drug Interdiction Auto Stop) cases in the USA
• Katz et al. test GPT-4 and its earlier progenitors on the three components of the bar exam, which in many US jurisdictions must be completed by a legally trained individual to be able to practise law.
• Hagan explores the integration of AI in the legal sector (particularly the justice sector) and emphasizes the importance of prioritizing community perspectives in AI design and policy-making.
• Yoon et al. explore the potential of AI to help reduce disputes. The authors challenge the optimistic view that AI can significantly improve litigation outcomes.

Complexity in legal systems is a top priority theme for someone interested in the (always debated) evolutionary increase in complexity, and who have published several short stories about artificial intelligence in legal pratices.

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Vivo, Pierpaolo, Daniel M. Katz, and J. B. Ruhl. 2024. ‘A Complexity Science Approach to Law and Governance’. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 382 (2270): 20230166. https://doi.org/10.1098/rsta.2023.0166.

Published by the Royal Society under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/4.0/, which permits unrestricted use, provided the original author and source are credited.

Featured Image: Lexica Art