3. Voting with two alternatives

A group of individuals selects one of two alternatives by voting, which may entail a cost. How do the individuals' decisions to vote depend on their preferences and voting costs? How does the fraction of individuals who vote depend on the population size? Voting is modeled as a strategic game. In this game, an individual's voting for her favored alternative is a dominant strategy. When voting is costly and each individual's voting cost is known only to her, the game has an equilibrium in which each individual votes only if her cost is at most some threshold. In this model, if the population is large, few individuals vote. However, if each individual votes so as to minimize her worst regret, rather than to maximize her expected payoff, a high turnout in a large population is possible.