Should law keep pace with society? Relative update rates determine the co-evolution of institutional punishment and citizen contributions to public goods

Until recently, theorists considering the evolution of human cooperation have paid little attention to institutional punishment, a defining feature of large-scale human societies. Compared to individually-administered punishment, institutional punishment offers a unique potential advantage: the ability to control how quickly legal rules of punishment evolve relative to social behavior that legal punishment regulates. However, at what rate should legal rules evolve relative to society to maximize compliance? We investigate this question by modeling the co-evolution of law and cooperation in a public goods game with centralized punishment. We vary the rate at which States update their legal punishment strategy relative to Citizens' updating of their contribution strategy and observe the effect on Citizen cooperation. We find that when States have unlimited resources, slower State updating lead to more Citizen cooperation: by updating more slowly, States force Citizens to adapt to the legal punishment rules. When States depend on Citizens to finance their punishment activities, however, we find evidence of a "Goldilocks" effect: optimal compliance is achieved when legal rules evolve at a critical evolutionary rate that is slow enough to force citizens to adapt, but fast enough to enable states to quickly respond to outbreaks of citizen lawlessness.