عدالت کور : تجزیه و تحلیل تجربی از مجازات به صورت تصادفی در تولید تیم

We study the effect of blind punishment in a team production experiment, in which subjects choose non-observable effort levels. In this setting, a random exclusion mechanism is introduced, linked to the normalized group performance (R, from 0 to 1). Every round, each subject is non-excluded from the collective profit with probability R (and with probability 1 − R gets no benefit from the group account). Punishment does not depend on the individual behavior, but the probability of being punished reflects collective performance. As the exclusion probability is computed at the group level, no individual information is needed to implement exclusion. However, the probabilistic punishment risks to be perceived by subjects as procedurally unfair, as all subjects are treated in an identical, non-equitable manner (justice is blind). Our results suggest that random exclusion promotes a significant increase in cooperation. The effect seems to be associated with hot behavioral responses to punishment. However, convergence to full contribution is not observed.

No group exists without norms, and norms are typically enforced by sanctions (see Posner & Rasmusen, 1999). This paper contributes to the experimental literature on social sanctions in social dilemmas, like public good games. This literature analyzes punishment in groups or teams, in which sanctions reduce both recipient and sender’s earnings, and tend to be considered as altruistic or social as it is a second-order public good. Punishment was first analyzed experimentally by Yamagishi (1988) using a centralized mechanism, vertically enforced. Subjects contributed to a punishment account that was used to punish free riders. Ostrom, Walker, and Gardner (1992) first introduced non-centralized punishment in a common-pool resource setting and Fehr and Gächter (2000) in a public good experiment.1 In these two papers punishment was carried out horizontally by individuals, not by a central authority. In all cases subjects were able to identify the full distribution of contributions in their group and punishment generated huge contribution gains. In this study, we specifically want to contribute to the understanding of enforcement mechanisms in teams when full information is not available.2 In many real life interactions, individual information is hardly accessible, or simply too costly. However, punishment still takes place (and makes sense as it enhances cooperation). Managers sanction some members of defective teams without knowing whom to blame for the poor performance. Residents in one area may ostracize certain defecting neighbors, without having full information about who is individually responsible for the lack of cooperativeness. Teachers sanction some students in a rebellious class even when they cannot find someone accountable for the revolt. This mechanism is as old as the Roman army, in which generals (tribunes) punished one tenth of the soldiers in a legion to encourage discipline and fight cowardice.3 Note that in the examples above, managers, neighbors, teachers or tribunes choose in a random way, whom to punish. Justice is in this sense blind, as long as it cannot identify individual defectors. Some individuals are sanctioned, depending on facts of random nature (who is coming first to the managers’ office, who is visiting the neighborhood, who is talking in the first row in class when the teacher turns around). All these examples have three additional interesting features. First, punishment is still social, in the sense that it pursues a collective goal. Second, not all team members are punished, because this is probably not necessary, maybe impossible or simply too costly. Third, even when sanctions are not linked to individual behavior, punishment still depends on the collective performance. Managers or teachers know the collective outcome and punish accordingly. So, the probability of being punished typically depends on the team’s performance. Good teams (brave legions) are never punished.4 It is interesting to notice that randomness has already been considered from a theoretical point of view. Rasmusen (1987) proposes two contracts to achieve efficiency in teams: “massacre” and “scapegoat”. In the former, all but one member (randomly chosen) of the team are penalized to pay a positive amount of money to the survivor, which in addition collects the joint product. In the latter, all but one (randomly chosen) shares the joint product and the penalty paid by the Guinean pig. Both mechanisms take advantage of risk aversion by fitting in random payoffs; i.e. players face a lottery in which with some positive probability they get negative payoffs.5 A growing related literature has applied this idea to environmental issues.6 In this paper we study a punishment mechanism based on random exclusions. Exclusion is a rather common disciplinary measure in many real life situations. Shirking workers are fired (Shapiro & Stiglitz, 1984); uncooperative neighbors are not invited to social events; societal defectors are incarcerated or expelled (Hirshleifer & Rasmusen, 1989); and countries that violate international conventions are boycotted. In our design, every team member faces a common probability of being excluded from the team benefit, as high as one (as low as zero), when collective contribution to the joint outcome is 0% (100%) of their total endowment. Punishment realizations are i.i.d. across team members. To test for the effectiveness of this random punishment mechanism, we run three different games in two alternative ways. A standard public good game based on the voluntary contribution mechanism (VCM) serves as a natural baseline. Relative to our benchmark treatment we test a random exclusion mechanism, with and without redistribution of the excluded share (as in Croson, Fatas, and Neugebauer (2006)). This design allows for a between subjects analysis across all three games. In addition, and to test for the role of random exclusion in overcoming cooperation failure,7 the random punishment mechanism is introduced in some sessions after a common history of cooperation collapse (the VCM game). This allows for an additional within subjects analysis across games within the same sessions. Croson et al. (2006) analyze a similar exclusion mechanism in different team production games.8 In all games, punishment is deterministic, and based on competitive exclusion. The worst performer is excluded from the benefits of team production, so a competition between group members determines who is (not) going to be punished. Their experimental results show that excludability produces large increases in contribution. Note that even when full information about individual contributions is not needed to implement exclusion in this setting, an ordinal ranking of individual contributions is still necessary. In our design, and contrary to Croson et al. (2006), exclusion is not based on competition. Some subjects are excluded from the collective benefit, but exclusion is not based on the relative performance of team members inside the team. Moreover, random punishment does not depend on the willingness to pay for punishing. This makes the success (or failure) of the mechanism independent of the existence of strong punishers. As it has been explained before, the individual information requirements are kept at a minimum. Within each group, all members share the same probability of being punished, so strictly speaking, no individual information is needed for the mechanism to be implemented. As far as we know, no experimental analysis of random punishment in teams has ever been done. An alternative random mechanism experimentally studied is random monitoring. Among many others, Nalbantian and Schotter (1997) experimentally tested it, reproducing the forcing contract proposed by Holmstrom (1982). The main differences between our design and random monitoring is that while individual information is obtained with random inspection, individual decisions are never used in our experiment. Moreover, sanctions coming from random monitoring are never random (cooperators are never punished). In addition, as Nalbantian and Schotter (1997) suggest, ‘unless the probability of detection is great (and, therefore, costly to maintain), such monitoring schemes are likely to fail’ (p. 316). In this sense, our random punishment is less demanding than random monitoring, from an informational point of view. We want to test whether it is more efficient. We are aware of the practical limitations of this mechanism, mainly coming from its unfair nature. Regardless of their individual behavior, all individuals face the same probability of being sanctioned. As in any other public good game, free riders still get an equal share of the collective benefits (if they are not punished). In our experiment, defectors also generate a public bad: their low contributions produce a negative externality (random punishment). This unfair mechanism may deteriorate the ‘motivational capital’ of a firm, using the term of Akerlof and Kranton (2005). As Prendergast (1999) puts it, the success of organizations depends on members’ willingness to take unselfish, efficiency enhancing actions. In this sense, blind punishment could easily harm the basis of public good provision in games: conditional cooperation.9 Random exclusions may lower contributions to the public good by cooperative subjects, as they can now be excluded from the public good benefits.10 So, we explicitly want to test whether the potential benefits of exclusions on contributions may disappear through the back door of a negative behavioral reaction to its blind, unfair nature. Our results suggest that random punishment promotes efficiency in a significant way. Between subjects, random exclusion generates more public good provision (with and without redistribution). Within subjects, random exclusion survives a past experience of contribution failure, as a significant increase is always observed. These results cannot be explained by risk attitudes. A deeper behavioral analysis suggests that cooperative subjects negatively react to sanctions, when punished. However, conditional cooperation survives to the use of blind sanctions, generating a net positive effect. The rest of the paper is as follows. Section 2 describes our experimental game, and provides a theoretical background. Section 3 analyzes decisions, earnings and behavioral patterns and Section 4 concludes.

Groups sanction defectors. Sometimes they do it on an individual basis, making free riders to contribute, as Croson et al. (2006) shows. Sometimes individual information is not available but individuals still punish members depending on their collective performance. In this paper, we have analyzed the impact of random punishment in an experimental public good setting. Each round, a member of a group receives her share of the public good with a probability that matches the relative aggregate contribution to the public good. The main advantage of random punishment relative to other punishment schemes considered in the literature is that the information requirements are low: no information at individual level is required at all. Hence, a mechanism of this sort seems especially applicable in situations where only information on the group level is available. In our experiments, random sanctions do not eliminate the usual contribution decline, but contributions are significantly larger than in a baseline without any random sanction. Moreover, this result is independent of the way the excluded share is distributed (or not distributed at all) among group members. However, the minimal informational requirements impose a kind of a compromise between information (the input feeding random exclusion) and efficiency (the output) of the mechanism. In other words, we minimize the informational requirements at a cost. Free riders and co-operators within the same group will be treated equally, and punished with the same probability. It seems natural to consider that the blindness nature of the mechanism might jeopardize the basis of public good provision in games: conditional cooperation. A conditional co-operator contributes to the public good as long as she observes others contributing. In a public good game with horizontal punishment, conditional co-operators may punish free riders to eliminate the advantages of defection. In a public good game with blind sanctions, punishment is not driven by individual behaviour but by collective performance. So, random exclusions might lower contributions to the public good by cooperative subjects if they anticipate that both co-operators and free riders will be excluded from the public goods benefits with the same common probability. Our experimental results support the positive rationale of using this unfair rule, in the sense that even when top contributors negatively react to being unfairly treated, punishment generates significant contributions gains. We want to finish the paper with the following straightforward interpretation of our findings: blind justice is better than no justice at all. Conditional co-operators survive the perverse effects of random punishment and are able to generate large contribution gains, even when defectors do not take the hint when punished.