The flip side of power

In random voting, the committee chair, whose vote decides in the case of a draw, is more often decisive than ordinary voters. Therefore, in the power indices literature, the committee chair is said to be more powerful. Players with a veto right are even more powerful still. Similarly, the production of threshold public goods may involve “tie-breaking players” (with more effective contributions) and “veto players” (specialists or larger players) whose contributions are necessary. We pose the question of whether power is beneficial for an individual. Except in the equilibrium where no player contributes, veto players are disadvantaged while tie-breaking players can be advantaged. In experiments with otherwise symmetric players, about 80% of the veto players contribute, but tie-breaking players also contribute almost as frequently as veto players, and significantly more frequently than ordinary players. Even with three times the costs of ordinary players, veto players stick to their behavior, while tie-breaking players reduce their contributions below those of ordinary players. Overall, powerful players always are worse off than ordinary players; thus, power seems not to pay off herein.

Common Knowledge Promotes Cooperation in the Threshold Public Goods Game by Reducing Uncertainty

Recent work suggests that an important cognitive mechanism promoting coordination is common knowledge—a heuristic for representing recursive mental states. Yet, we know little about how common knowledge promotes coordination. We propose that common knowledge increases coordination by reducing uncertainty about others’ cooperative behavior. We examine how common knowledge increases cooperation in the context of a threshold public goods game, a public good game in which a minimum level of contribution—a threshold—is required. Across two preregistered studies (N = 4,111), we explored how varying (1) the information participants had regarding what their group members knew about the threshold and (2) the threshold level affected contributions. We found that participants were more likely to contribute to the public good when there was common knowledge of the threshold than private knowledge. Using structural equation modeling, we found that the predicted number of group members contributing to the public good and certainty about the predicted number of contributors mediated the effect of information condition on contributions. Our results suggest that common knowledge of the threshold increases public good contributions by reducing uncertainty around other people’s cooperative behavior. These findings point to the influential role of common knowledge in helping to solve large-scale cooperation problems.