Scaling laws: legal and social complexity in US localities

Law sets out the rules for society and the economy, particularly important for interactions between strangers. Legal code is a form of non-rival infrastructure, a public good important for investment and innovation. This paper investigates whether legal code complexity scales with population size in US localities. We analyse a corpus of municipal codes from 3259 cities and measure legal complexity using various metrics, including number of words, bytes, and compressed bytes. We find that legal complexity scales geometrically with jurisdiction population, with a scaling parameter of approximately 0.2 and an R2 of approximately 0.2. The estimated scaling parameter is similar to gross domestic product per capita, consistent with an interpretation of legal codes as regulating social interactions per capita in cities.This article is part of the theme issue 'A complexity science approach to law and governance'.