Question 9.67

37. An interesting variant of the Hare system was proposed by psychologist Clyde Coombs. It operates exactly as the Hare system, but instead of deleting alternatives with the fewest first-place votes, it deletes those with the most last-place votes.

  1. Use the Coombs procedure to find the winner if the ballots are as in Exercise 36.
  2. Show that for two voters and three alternatives, it is possible to have ballots that result in one candidate winning if the Coombs procedure is used and a tie between the other two if the Hare system is used.

37.

(a)

(b) Answers will vary.