Threshold behavior of a social norm in response to error proneness

Abstract: A social norm defines what is good and what is bad in social contexts, as well as what to do based on such assessments. A stable social norm should be maintained against errors committed by its players. In addition, individuals may have different probabilities of errors in following the norm, and a social norm would be unstable if it benefited those who do not follow the norm carefully. In this work, we show that Simple Standing, which has been known to resist errors and mutants successfully, actually exhibits threshold behavior. That is, in a population of individuals playing the donation game according to Simple Standing, the residents can suppress the invasion of mutants with higher error proneness only if the residents' own error proneness is sufficiently low. Otherwise, the population will be invaded by mutants that commit assessment errors more frequently, and a series of such invasions will eventually undermine the existing social norm. This study suggests that the stability analysis of a social norm may have a different picture if the probability of error itself is regarded as an individual attribute.