Three candidates are running for mayor. A vote was taken in which the candidates were ranked in order of preference. The results are shown in the preference schedule below. Rankings John Lorenz 1 3 3 Marcia Beasley 3 1 2 Stephen Hyde 2 2 1 Number of votes: 2525 2288 227 (a) Use the Borda Count method to determine the winner of the election. John Lorenz Marcia Beasley Stephen Hyde There is a tie between Marcia Beasley and Stephen Hyde. There is a tie between John Lorenz and Stephen Hyde.

(b) Verify that the majority criterion has been violated. John Lorenz received the fewest number of first-place votes. Marcia Beasley received the fewest number of first-place votes. Stephen Hyde received the fewest number of first-place votes. Marcia Beasley received no first-place votes. John Lorenz received no first-place votes.

(c) Identify a candidate who wins all head-to-head comparisons. John Lorenz Marcia Beasley Stephen Hyde There is a tie between Marcia Beasley and Stephen Hyde. There is a tie between John Lorenz and Marcia Beasley.

(d) Explain why the Condorcet criterion has been violated. There is not a tie for first-place. The candidate that wins all the head-to-head matches does not win the election. No candidate got all of the votes. The candidate that finishes in third-place should have won. There is not a tie for second-place.

(e) If Marcia Beasley drops out of the race for mayor (and voter preferences remain the same), determine the winner of the election again, using the Borda Count method. John Lorenz Marcia Beasley Stephen Hyde There is a tie between Marcia Beasley and Stephen Hyde. There is a tie between John Lorenz and Stephen Hyde.

(f) Explain why the independence of irrelevant alternatives criterion has been violated. The candidate winning the original election remained the winner in a recount in which a losing candidate withdrew from the race. The candidate winning the original election did not remain the winner in a recount in which a losing candidate withdrew from the race. Two candidates got the same number of votes. The candidate that withdrew won the election. Since there were not three candidates, there has to be a re-vote.