Majority Voting Over Lotteries: Conditions for Existence of a Decisive Voter

This note extends known sufficient conditions for existence of a decisive voter in pairwise voting over lotteries. The preferred lottery of such a voter always coincides with the lottery preferred by a majority, meaning voting can be reduced to a decision problem of the decisive voter. The results are useful in solving dynamic models of bargaining and elections, where a binary vote can be expressed as a choice between two lotteries (depending on the discount factor), and voting subgames can be reduced to a decision problem of the decisive voter.