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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.

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Fig. 1: Framing contrasting scales of decision-making and public goods.
Fig. 2: Levels of institution participation and of cooperation inside and outside the institution.
Fig. 3: Stationary levels of institution adoption and cooperation for the different configurations of information and memory as a function of the quorum.
Fig. 4: A collection of experimental results.

Data availability

Data sources for experimental results are detailed in Supplementary Section F.

Code availability

Pseudocode for the computational model is available in Supplementary Section A. Code for the simulations is available in the GitHub repository:


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V.V.V. acknowledges funds from the Princeton Institute for International and Regional Studies, through the Rapid Switch Initiative. V.V.V. and S.A.L. acknowledge funding from the US Defense Advanced Research Projects Agency (D17AC00005) and National Science Foundation grant GEO-1211972. A.D. acknowledges funding from the European Union (EU) Horizon 2020 programme, action ERC-2014-STG, Project HUCO, grant number 636746.

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Authors and Affiliations



V.V.V, A.D. and S.A.L. discussed the design, analysis and results. A.D. compiled the experimental results data. V.V.V. designed and analysed the model and data. V.V.V. and A.D. wrote the paper.

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Correspondence to Vítor V. Vasconcelos.

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Nature Sustainability thanks the anonymous reviewers for their contribution to the peer review of this work.

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Supplementary Sections A–F.

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Vasconcelos, V.V., Dannenberg, A. & Levin, S.A. Punishment institutions selected and sustained through voting and learning. Nat Sustain 5, 578–585 (2022).

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