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.

在随机投票中，在抽签的情况下由其投票决定的委员会主席通常比普通选民更具决定性。因此，在权力指数文献中，委员会主席的权力更大。拥有否决权的玩家甚至更强大。同样，门槛公共产品的生产可能涉及“打破平局的参与者”（具有更有效的贡献）和“否决参与者”（专家或更大的参与者），其贡献是必要的。我们提出权力是否对个人有益的问题。除了在没有玩家贡献的均衡中，否决玩家处于劣势，而打破平局的玩家可以处于优势。在其他对称球员的实验中，大约 80% 的否决球员做出了贡献，但打破平局的球员也几乎与否决球员的贡献一样频繁，并且明显比普通玩家更频繁。即使成本是普通玩家的三倍，否决玩家还是坚持自己的行为，而打破平局的玩家则将贡献降低到普通玩家以下。总的来说，强大的玩家总是比普通玩家差；因此，权力在这里似乎没有回报。