Question 10.35

5. There are at least three voting systems for two candidates ( and ) and three voters that are nonmanipulable and that treat both candidates the same (meaning that if all three voters change their ballots, then the election outcome also changes).

  1. What does May's theorem tell us about such a voting system?
  2. In one sentence, give an example of such a voting system (i.e., produce the rule that determines which of the two candidates wins an election).
  3. In one sentence, give two other examples that are different from the example you gave in part (b) in that they produce a different winner for at least one election.

5.

(a) The voting system does not treat all voters the same.

(b) A dictatorship in which Voter 1 is the dictator.

(c) A dictatorship in which Voter 2 is the dictator and a dictatorship in which Voter 3 is the dictator.