Punishment institutions selected and sustained through voting and learning

In virtually all human societies, the sustained provision of public goods is enforced through punishment. This can happen, for example, via a legal system (formal punishment institutions) or individual-level reciprocity (informal punishment institutions). However, targeting and enforcement of punishment is usually costly, leaving a permanent temptation for individuals to avoid the costs. Here, we show that costly punishment institutions can be adopted through voting and learning but suffer an existential threat if the decision-making process to implement the punishment institution is not aligned with the scale of the public good, creating unavoidable free-riding incentives. We design a model where individuals vote in favour of or against the institution, either with their feet or group vote, to govern public goods at different scales. Learning occurs through the accumulation of one’s experiences and observations of other members in the population, but it may be limited due to memory and information constraints. We show—across scales of the decision-making process and public good—under which conditions punishment institutions are adopted and promote cooperation. Using a meta-study approach, we compare the model to existing experimental results, which largely confirm the key results of the model.