Pivotal Players and the Characterization of Influence

A player's influence relative to a mechanism and opponents' strategies is the maximum difference his action can make in the expected value of a collective outcome. A player is :-pivotal if his influence exceeds a threshold :. We provide tight bounds on the number of pivotal players and on average influence. These bounds are uniform over all mechanisms and action profiles and are achieved at mechanisms that take the form of a majority rule. We illustrate our analysis with an example of provision of a public good where each individual compares the private cost of his contribution with its influence on the collective outcome. Journal of Economic Literature Classification Numbers: D62, D89, H41. 2000 Academic Press