Voting on two alternatives appears unproblematic compared to voting on three (or more). When faced with only two alternatives, many arguments show that Majority Rule distinguishes itself from all other ways of making a group decision. For three or more alternatives, one faces the so-called “Paradox of Voting”: there may be elections with a majority cycle in which a majority of voters prefer A to B, a majority of voters prefer B to C, and a majority of voters prefer C to A. In this talk, I will explain a series of results that axiomatically characterize rules for resolving majority cycles in elections. These rules avoid the “Strong No Show Paradox” by responding properly to the addition of new voters to an election and mitigate spoiler effects by responding properly to the addition of new candidates to an election.

This talk is based on joint work with Wes Holliday.