![]() 20 examine the pool punishment system by implementing it in a laboratory experiment and show that participants tend to select pool punishment over peer punishment. The authors mathematically show that the pool punishment system is more stable than peer punishment only when the system punishes both the first- and second-order free riders (the latter do not bear the cost of the punishment system). 18 compares peer punishment with pool punishment, in which group members pay costs to a punishment-executing system (e.g., a police force) and the system uses these resources as capital to punish free riders. Other than the peer punishment system, the pool punishment system has been proposed to solve the public goods problem 16, 17, 18, 19, 20. As such, there is much doubt as to whether peer punishment solely can solve the public goods problem. Furthermore, an anthropological survey showed that punishment between individuals is rare in a small society, which is similar to an evolved environment 15. However, both theories have been criticized (Pinker’s criticism 13 for multi-level selection Raihani and Bshary’s criticism 14 for punishers’ reputations) and there is no sufficient answer yet. The reasons people punish, even if they have to pay the cost, have been proposed using multi-level selection theory 10 and reputational benefits for punishers 11, 12. Thus, in theory, peer punishment should not evolve. However, because the individual’s profits increase if s/he punishes nobody, second-order free riders emerge. Because punishing someone incurs cost, owing the punishment cost to maintain group cooperation is a second-order cooperative action. The biggest theoretical issue is the second-order free rider problem 8, 9. Despite several laboratory experiments indicating that peer punishment solves the free rider problem 3, 4, 5, 6, several theoretical and empirical questions have been posed. This involves individuals punishing free riders, which decreases the incentive to free ride and, thus, establishes cooperation 7. ![]() Peer punishment is one solution proposed by scholars 3, 4, 5, 6. In modern times, such PGG situations range widely from small-scale issues, like housework distribution within a household, to large-scale ones, like acts to prevent global warming. In historical times, PGG situations involved food distribution in hunter–gatherer societies and irrigation facility work in agrarian societies. Humans encounter many PGG situations in daily life. ![]() This results in a socially inefficient situation. Free riders, however, can increase their own payoff if they contribute nothing and still benefit from the common pool. The entire group earns the highest profit when all members contribute all their resources. In a typical public goods game (PGG), group members decide how much of their own resources to contribute to the common pool and the resources gathered in the pool benefit members equally. The difficulties of constructing a cooperative relationship are formulized as a public goods problem 1, 2, and many such studies are conducted in the social sciences. This means that leaders who effectively punish followers could increase their own benefits and the second-order free rider problem would be solved. ![]() In addition, linkage-type leaders themselves earn higher profits than other leader types because they withdraw more support. Within the former, both higher cooperation and higher support for a leader are achieved under linkage-type leaders-who punish both non-cooperators and non-supporters. The results show that punishment occurs more frequently in the support-present condition than the no-support condition. We compare a support-present condition with a no-support condition, in which there is an external source for the leader’s punishment. In our experiment, participants engage in three stages repeatedly: a PGG stage in which followers decide to cooperate for their group a support stage in which followers decide whether to support the leader and a punishment stage in which the leader can punish any follower. Here we introduce a “leader support system,” in which one group leader can freely punish group followers using capital pooled through the support of group followers. However, second-order free riders, who do not pay punishment costs, reduce the effectiveness of punishment. Punishment of non-cooperators-free riders-can lead to high cooperation in public goods games (PGG).
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