Barriers to Manipulation in Voting

Example 6.1. Consider an election with three alternatives, a, b, and c, and three voters, 1, 2, and 3. Suppose the rule used is plurality—an alternative gets a point each time it is ranked first by a voter, and the alternative with the most points wins—with ties broken toward alternatives earlier in the alphabet. Suppose voter 3 knows (or strongly suspects) that voter 1 will rank a first in her vote, and that voter 2 will rank b first. Voter 3’s true preferences are c b a. If she votes truthfully, this will result in a three-way tie, broken in favor of a which is 3’s least preferred alternative. If, instead, voter 3 ranks b first, then b will win instead. Hence, voter 3 has an incentive to cast a vote that does not reflect her true preferences.