کمک های داوطلبانه با توزیع مجدد: اثر تحریم های پرهزینه که مجازات یک نفر را پاداش دیگری است

We introduce new treatments of a voluntary contribution mechanism with opportunities to punish in order to see how contributions, punishments and earnings change when punishment is in the form of fines the punisher distributes to other members of her group. The linked punishment-reward set up is of theoretical interest and could represent simultaneous shifts of social disapproval and approval. Conjectures that punishment will be better targeted, and that it will be more substantial for given deviation from others’ contributions, receive support. Making punishment redistributive increases contributions and efficiency, even after netting out the design's free resource element.

One of the most active areas of experimental economics research in recent years has been the exploration of subjects’ propensities to engage in costly punishment and the impact of punishment on a variety of interactions, including public goods and common pool resource dilemmas.1 Punishment is of interest both for the practical reason that it may play a pivotal role in solving these and other dilemma problems by creating self-interested incentives to take socially efficient actions (Fehr and Gächter, 2000, Gürerk et al., 2006 and Gächter et al., 2008), and because evidence of its presence is suggestive of a preference or predisposition that may have even broader implications for both theory and policy. Indeed, some argue that human cooperation in matters as varied as the exertion of effort in workplaces and partnerships and the functioning of states would be impossible but for the widespread presence of the impulse to punish free riders (Field, 2001, Fehr and Schmidt, 2003 and Gintis et al., 2005). Although willingness to pay for punishment and its often pronounced effect on voluntary contributions are remarkable, authors including Cinyabuguma et al. (2004), Cinyabugama et al. (2006), Botelho et al. (2005), Gächter and Herrmann (2005), and Herrmann et al. (2008) have pointed out that allowing punishment in public goods experiments can have a far less salutary effect on earnings, hence efficiency. Since earnings rise with contributions but fall with expenditures on and earnings lost to punishment, a central question about the efficiency impact of an option to punish is whether there is a high enough ratio of contributions induced by the threat of punishment to costs associated with punishment actually carried out. Theoretically, if only low contributors are threatened with punishment and if the threat is well anticipated, little or no actual punishment would be needed in order for the existence of a punishment opportunity to raise both contributions and earnings.2 There is evidence that subjects do increase contributions when punishment is available, even before observing it. However, in the numerous experiments in the literature, substantial punishment costs are incurred by punishers and those targeted by them, depressing aggregate earnings. As Gächter and Herrmann (2008) put it in their comprehensive review of the voluntary contributions literature: “In most experiments in which punishment has material pay-off consequences, punishment turned out to be an inefficient tool to enforce cooperation because resources are destroyed.” In addition to the amount of punishment that is required to get the job done, mis-targeting of punishment can also lower efficiency. Cinyabugama et al. (2006), Gächter et al. (2005), Herrmann et al. (2008) and Ertan et al. (2009) provide evidence that a major reason for the sometimes inefficient impact of decentralized punishment is that a substantial fraction of it is misdirected at high contributors—a phenomenon that we call “perverse punishment” and that overlaps with what Herrmann et al. call “anti-social punishment.”3 In 13 of 16 subject pools around the world in which those authors conducted voluntary contribution experiments both with and without punishment, earnings were lower in the punishment condition. In their experiments, the difference between earnings in the no punishment and in the punishment conditions was highly correlated, at the subject pool level, with the proportion of punishment classified as “anti-social.” A desire to investigate ways to reduce or offset perverse punishment is an important motivation of the present research. Sefton et al. (2007), and Sutter et al. (2010) studied settings in which subjects could reward rather than punish group members in a voluntary contributions game and compared the effectiveness of rewards to that of punishment. Both studies found rewards to be less effective than punishment when the rewarding technology is revenue neutral (it costs the bestower one unit to give one additional unit of earnings to the beneficiary).4 When Andreoni et al. (2003) studied rewards and punishment separately in one-shot proposer-responder games, they similarly found that “rewards are much less effective in moving the proposers away from the minimum possible offer (p. 894).” Andreoni et al. also studied the combination of rewards and punishment and found it to be more effective than either device by itself. To our knowledge, costly rewards and punishment have not been combined in the voluntary contributions game, although cost-free redistribution is studied by Sausgruber and Tyran (2007), who find that it elicits significantly higher contributions and hence efficiency. The purpose of the present paper is to study the impact of costly punishment when resources lost to the punished party must be transferred by the punisher to some other member or members of the group. Ceteris paribus, this way of combining rewards with punishments is more efficient than treatments in which penalties “vanish” or “are burned,” since no additional resources are lost other than the costs to punishers. 5 Its incentive impact is also likely to be greater than that of punishment alone, since the punisher can reward cooperators at no additional cost at the same time as she punishes free riders. But that outcome is assured only if punishment is targeted properly, which brings us back to our concern with the perverse targeting of punishment. The subset of punishers observed to punish high contributors in other public goods experiments could conceivably do even more damage by not only punishing “good behavior” but also rewarding “bad.” In the cost-free redistribution treatment of Sausgruber and Tyran, 15% of redistribution events involve taking from a high and giving to a low contributor. Such behavior could have more deleterious effects if observed at the higher frequencies with which perverse or anti-social punishment is sometimes found. We conjectured, however, that if making costly punishment redistributive had any effect on the targeting of punishment, it would be an ameliorative one, reducing the incidence of perverse and anti-social punishment. Consider separately the motivations behind the punishing of free riders and the perverse punishing of high contributors. Suppose that punishment of free riders can be attributed to two main motivations: (a) a desire to punish norm violators and perhaps to increase group efficiency, and (b) inequality aversion. An individual contemplating punishing a free rider for either of these reasons should have an even greater incentive to do so if she can simultaneously reward cooperators at no extra expense. Moreover, subjects concerned with efficiency in the sense of Charness and Rabin (2002) should punish more when the efficiency loss is lessened by the losses of punished group members being redistributed rather than “burned.” In contrast to normal punishment, the perverse punishment of high contributors may be explained by two rather different motivations: (a) to avenge and possibly head off being punished for free riding, and (b) to increase one's own earnings relative to the earnings of other group members. Neither motive for punishing perversely is reinforced by a requirement that earnings taken from high contributors be redistributed to other group members besides oneself. When the identity of your punisher is unknown, rewarding a low contributor, whom you least suspect of being your punisher, does nothing to help with goal (a), and using the losses of a punishment-receiving high contributor to reward a free rider threatens to raise the latter's earnings above your own, contrary to (b). Accordingly, it seemed that redistributive punishment would if anything reduce the share of punishment aimed at cooperators. It is natural to ask whether our new treatment bears any relationship to real world phenomena. We have thus far been unable to identify collective action settings that feature peer-on-peer seizure of resources that are then conferred on others, but the approach might be worth trying in, for instance, some work-group settings. Moreover, the destruction of a fellow group-member's wealth or earnings by costly punishment also lacks a concrete counterpart in many real world collective action settings (for instance, profit-sharing teams or partnerships), where thinking of sanctions as proxying for social penalties like shunning or criticizing is more plausible. Insofar as this is so, it may not be a great stretch to say that redistributive punishment is in fact widely observed in the form of the elevation of the respect or social status of some (e.g., cooperators) that often accompanies the lowering of that of others (non-cooperators).6 Whatever one's judgment of real world application, our new treatment is potentially of interest for shedding light on the motivations behind punishment. Our results are qualitatively consistent with the conjecture that making punishment redistributive reduces both the amounts and the number of instances of punishment going either to groups’ highest contributors or to contributors of more than their group average for the period; the differences, however, are not statistically significant. When we consider punishment from the recipients’ standpoint—that is, consider the sum of all punishment aimed at an individual minus any rewards the individual receives, the separate components not being observable by the individual targeted in our design—the proportion of net punishment dollars aimed at high contributors is lower in the redistributive treatment. This difference is significant if attention is restricted to punishment of highest contributors. Making punishment redistributive is thus efficiency-enhancing, although the difference is statistically significant only when we incorporate the reinforcing effect of the pattern of rewards into the analysis. When evaluating the efficiency impact of making punishment redistributive, it is necessary to recognize that that innovation has a built-in resource effect that calls for careful evaluation. To compare in a more neutral way the efficiency achieved in treatments with redistribution and that of treatments without redistribution, we net out the differences in the direct resource difference from “throwing away” vs. redistributing punishment costs. We find that having one subject's earnings reductions (penalties) be distributed to others has not only the direct resource benefit inherent in this mechanism but also an incentive benefit that raises efficiency by encouraging more contributions to the public good. This pure incentive impact on efficiency is small but is at least marginally statistically significant. The rest of the paper proceeds as follows. In Section 2, we give details of the experimental design. In Section 3, we discuss relevant theoretical issues and predictions. Section 4 describes and analyzes the results of the experiment. Section 5 provides further discussion and conclusions.

We conjectured that if subjects given opportunities to impose costly punishment in a public goods or VCM experiment were required to redistribute the targeted individuals’ losses to other group members, this would spur more punishment by “pro-social” punishers, lessen the share of punishment going to high contributors, and raise efficiency accordingly. Our conjecture was on the whole supported. Even after controlling for the higher efficiency associated with the retention of resources for redistribution, efficiency is greater in the redistributive treatment, in which both punishment and rewards are well targeted to spur higher contributions—although the difference is only marginally statistically significant. In the real world, punishment of free riders and rewarding of cooperators are often observed in tandem, including in cases where punishment and rewards take the forms of social disapproval and approval. Fines levied on norm violators can be used to finance goods that cooperators value, although it's difficult to think of cases in which pecuniary or material punishment is both decentralized (that is, left to individuals, sometimes called “informal sanctions”) and redistributive. Centralized redistribution from low to high contributors is automatically effected by the mechanism studied by Falkinger et al. (2000). Similar rules are spontaneously proposed and implemented by subjects given the opportunity to be mechanism designers in a study by Rockenbach and Wolff (2009).29 And cost-free decentralized redistribution is studied and found to boost efficiency by Sausgruber and Tyran (2007). When rewards are sufficiently sure to be transferred from low contributors to high ones, it becomes incentive compatible to contribute, and the problem of free riding should in principle disappear. We began this paper by pointing out that allowing subjects to punish other members of their group has often increased contributions but not earnings. For example, earnings in the P treatment discussed in this paper are not higher than those in a counterpart treatment without punishment opportunities studied by Page et al. (2005) as their Baseline or B treatment.30 Does making punishment redistributive do a better job of raising earnings relative to that no-punishment B treatment than the P treatment does? Two-tailed Mann–Whitney tests show that earnings are higher in the RP treatment than in the B treatment of Page et al., significant at the 0.1% level (U = 9.0) before eliminating the resource advantage of conserved resources, and at the 1% level (U = 33.0) after subtracting off reward earnings. This supports the conclusion that by reducing perverse punishment and increasing incentives to raise contributions, redistributive punishment increases efficiency where punishment alone fails to do so. At the most general level, our study provides more evidence, consistent with Ostrom et al. (1992), Fehr and Gächter (2000), Carpenter and Matthews (2002), Page et al. (2005), Falk et al. (2005), Gürerk et al. (2006), Sefton et al. (2007), Nikiforakis and Normann (2008) and others, that many individuals’ choices display positive and negative reciprocity (conditionally cooperating, and incurring cost to punish free riders), and that the existence of such individuals can ameliorate free riding problems by rendering it best for selfish individuals to cooperate and by supporting, in this way, conditional cooperators’ inclinations to contribute. However, like Cinyabugama et al. (2006) and Herrmann et al. (2008), we also find a subset of individuals who perversely punish cooperators, reducing the incentives of the latter to voluntarily contribute to a public good. Our experiment shows that reducing the incentive to engage in perverse punishment and reducing perverse punishment's net effect by making punishment redistributive is one way to ameliorate the negative impact of this phenomenon.