When do we punish people who don't?

People often punish norm violations. In what cases is such punishment viewed as normative-a behavior that we "should" or even "must" engage in? We approach this question by asking when people who fail to punish a norm violator are, themselves, punished. (For instance, a boss who fails to punish transgressive employees might, herself, be fired.) We conducted experiments exploring the contexts in which higher-order punishment occurs, using both incentivized economic games and hypothetical vignettes describing everyday situations. We presented participants with cases in which an individual fails to punish a transgressor, either as a victim (second party) or as an observer (third party). Across studies, we consistently observed higher-order punishment of non-punishing observers. Higher-order punishment of non-punishing victims, however, was consistently weaker, and sometimes non-existent. These results demonstrate the selective application of higher-order punishment, provide a new perspective on the psychological mechanisms that support it, and provide some clues regarding its function.