Estimating the efficacy of a vote

The efficacy of a vote by an individual citizen in an election may be defined roughly as the expected effect it has on the outcome of the election. This is a measure of how much that voter contributes to the decision making of the social system in which he is. A number of political scientists have rightly claimed that the efficacy of a vote is small when the electorate is large. We argue here that they have somewhat misdefined an important parameter of the problem and we strengthen their work by means of a Bayesian analysis. Many people derive personal utility from the act of voting quite apart from the efficacy of the vote as such. This analysis depends primarily on the voter's estimate of the probability that his vote will either produce or resolve a tie. The asymptotic form for this probability is quite different from one that has appeared in the literature. The probability is tabulated on the assumption of a beta prior and the problem of choosing the parameters in this distribution is analyzed.