Group Size Effect and Over-Punishment in the Case of Third Party Enforcement of Social Norms

One of the important topics in public choice is how people’s free-riding behavior could differ by group size in collective action dilemmas. This paper experimentally studies how the strength of third party punishment in a prisoner’s dilemma could differ by the number of third parties in a group. Our data indicate that as the number of third party punishers increases in a group, the average punishment intensity per third party punisher decreases. However, the decrease rate is very mild and therefore the size of total punishment in a group substantially increases with an increase in group size. As a result, third party punishment becomes a sufficient deterrent against a player selecting defection in the prisoner’s dilemma when the number of third party punishers is sufficiently large. Nevertheless, when there are too many third party punishers in a group, a defector’s expected payoff is far lower than that of a cooperator due to strong aggregate punishment, while some cooperators are even hurt through punishment. Therefore, the group incurs a huge efficiency loss. Such over-punishment results from third party punishers’ conditional punishment behaviors: their punishment intensity is positively correlated with their beliefs on the peers’ punitive actions. Some possible ways to coordinate punishment among peers even when group size is very large, thus enabling the efficiency loss to be mitigated, are also discussed in the paper.