Question 9.61

31. Suppose there are three voters and three alternatives , and .

  1. If each alternative has exactly one first-place vote, what is the election outcome if the Hare system is used? What if plurality runoff is used?
  2. If an alternative has two or more first-place votes, what is the election outcome if the Hare system is used? What if plurality runoff is used?
  3. Can the Hare system and plurality runoff yield different election outcomes when there are three voters and three alternatives? Explain your answer in one sentence.

31.

(a) A three-way tie with both methods

(b) In both the Hare procedure and plurality runoff, the candidate with 2 or more first-place votes will become the sole winner.

(c) No, either the situation in part (a) or the situation in part (b) must occur.