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 $R^2$ 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’.

法律规定了社会和经济的规则，对于陌生人之间的互动尤其重要。法律法规是一种非竞争性基础设施，是对投资和创新非常重要的公共产品。本文调查了美国各地法律代码的复杂性是否与人口规模成正比。我们分析了来自 3259 个城市的市政法规语料库，并使用各种指标（包括字数、字节数和压缩字节数）衡量法律复杂性。我们发现法律复杂性与辖区人口成几何比例，比例参数约为 0.2，比例参数约为 0.2。${右}^2$约为0.2。估计的缩放参数与人均国内生产总值类似， 与规范城市人均社会互动的法律法规的解释一致。

本文是主题“法律和治理的复杂性科学方法”的一部分。