The concepts of inequity aversion and of reciprocity both predict that punishment decisions will be influenced by the partner's behaviour. However, inequity aversion predicts that individuals are sensitive to how their payoffs compare with those of interaction partners, whereas the concept of reciprocity predicts that punishment decisions are influenced by how payoffs compare with individual expectations and are therefore independent of the relative payoffs gained by cheating partners. It is hard to disentangle whether punishment is motivated by a desire to reciprocate losses or by inequity aversion because players involved in interactions with cheats often simultaneously experience losses and inequity [9,10]. For example, evidence from laboratory public goods games (where contributions to a communal account are altruistic in the sense that they yield benefits to other group members at a cost to the donor; [11]) has shown that players experience anger and disgust when interacting with non-contributing (‘free-riding’) group members. The intensity of these emotions correlates with the propensity to administer costly punishment to reduce free-riders' incomes [4,12]. However, in such games, cooperative individuals (those who contribute to the communal account) experience absolute losses and lower payoffs relative to those of free-riders, meaning that it is not clear whether the negative emotions produced from interactions with cheats arise from a desire to reciprocate losses or from inequity aversion [10]. A more recent study used a random income game (where players were randomly allocated different-sized earnings) to show that punitive behaviour can be motivated by inequity, even in the absence of losses [12]. Low-earning players in this game experienced negative emotions targeted towards higher-earning counterparts and were willing to pay a cost to reduce the income of high earners [12]. Thus, punitive behaviour can arise even when higher-earning players do not impose losses on lower-earning individuals and when there is no cooperative norm to be enforced. In a subsequent study, it was shown that the tendency to reduce the income of high earners in a random income game is positively associated with the propensity to punish free-riders in public goods games [13]. While these findings indicate that punishment may be motivated by inequity aversion, neither study asked whether punishment might also be motivated by losses in the absence of inequity. We tested this possibility here.

Why do humans rely on a more cognitively complex task of monitoring their own payoffs relative to those of interaction partners, rather than simply monitoring their own payoffs relative to an internal expectation, when deciding whether to punish cheats? One possibility is that punishment promotes cooperative behaviour only if the punishment is deemed to be fair. This may only be the case when a cheat gains higher payoffs from the interaction than the victim as a consequence of the cheating behaviour. Victims of cheats may therefore do best to monitor how their payoffs compare with those of interaction partners before investing in costly punishment. Empirical evidence offers some support for this hypothesis. Using an experimental trust game with and without punishment, Fehr & Rockenbach [20] showed that the moral legitimacy of punishment has a striking effect on the prevalence of cooperative behaviour. In this game, one individual, an ‘investor’, can send money to another individual, a ‘trustee’. The money sent to the trustee is multiplied by the experimenter and the trustee can then choose how much of the entrusted amount to return to the investor. In their study [20], investors were allowed to stipulate how much of their initial investment they expected to receive back from the trustee and also whether they would fine the trustee for non-compliance. They found that fines for desired back-transfers that were deemed to be unfair largely undermined cooperative behaviour: trustees kept more of the invested amount under these conditions. This study suggests that punitive behaviour that is deemed to be unfair may not be accepted by the target. As well as failing to promote cooperative behaviour, punishment may also elicit retaliation from targets (cf. [21]), although it is not known whether retaliation is more likely when punishment is deemed to be unfair. This would be an interesting avenue for future investigation.