Abstract
Third-party punishment involves bystanders voluntarily incurring costs to punish norm violators, thereby maintaining social norms and cooperation. While prior research shows reduced punishment when the bystander and violator are friends, less is known about how the violator–victim relationship affects such punishment. Based on deterrence theory, punishment serves both to sanction violations and deter future threats. Accordingly, using the Dictator Game–third-party punishment paradigm across five experiments with a primary adult sample, this study investigated the impact of social relationships on third-party punishment, examined the mediating role of threat perception, and validated the applicability of deterrence theory within the context of third-party punishment. A pilot experiment confirmed that bystanders punish friends less than strangers. Experiment 1 showed that when the bystander and violator were friends, punishment was stronger if the violator and victim were also friends. Experiment 2 showed that congruent social relationships (e.g., all parties are friends) elicit greater punishment than incongruent ones. Experiment 3 demonstrated that threat perception mediates this effect: consistency increases threat perception, which in turn heightens punishment. In summary, consistency of social relationships increases third-party punishment, mediated by elevated threat perception. These findings support the use of deterrence theory in third-party punishment contexts and deepen our understanding of how social relationships shape punitive behavior.