Identifying mechanisms able to sustain costly cooperation among self-interested agents is a central problem across social and biological sciences. One possible solution is peer punishment: when agents have an opportunity to sanction defectors, classical behavioral experiments suggest that cooperation can take root. Overlooked from standard experimental designs, however, is the fact that real-world human punishment---the administration of justice---is intrinsically noisy. Here we show that stochastic punishment falls short of sustaining cooperation in the repeated public good game. As punishment noise increases, we find that contributions decrease and punishment efforts intensify, resulting in a 45% drop in gains compared to a noiseless control. Moreover, we observe that uncertainty causes a rise in antisocial punishment, a mutually harmful behavior previously associated with societies with a weak rule of law. Our approach brings to light challenges to cooperation that cannot be explained by economic rationality and strengthens the case for further investigations of the effect of noise---and not just bias---on human behavior.

The experiments were conducted from March to July 2021 using oTree. We recruited participants using the online platform Prolific.co. The sole reason for exclusion was prior participation in a study.  Participants were paid a fixed compensation of £3.75 with the opportunity to earn a bonus of up to £6 based on their income in the game. In total, 384 participants in 96 groups finished the experiment. After removing groups with repeated non-responses in order to eliminate bias, 80 groups remained for the analysis, involving 320 participants from 41 countries (sex ratio 2:1). These are distributed on the experimental conditions in the following way: 21 groups in the control condition, and 20 (resp. 20, 19) groups in the low (resp. medium, high) noise treatment condition.