Voting on punishment systems within a heterogeneous group

We consider a voluntary contributions game, in which players may punish others after contributions are made and observed. The productivity of contributions, as captured in the marginal-per-capita return, differs among individuals, so that there are two types: high and low productivity. Every two or eight periods, depending on the treatment, individuals vote on a punishment regime, in which certain individuals are permitted, but not required, to have punishment directed toward them. The punishment system can condition on type and contribution history. The results indicate that the most effective regime, in terms of contributions and earnings, is one that allows punishment of low contributors only, regardless of productivity. Nevertheless, only a minority of sessions converge to this system, indicating a tendency for the voting process to lead to suboptimal institutional choice.