Chapter 13 - Voting and Apportionment - 13.2 Flaws of Voting Methods - Exercise Set 13.2 - Page 861: 11

(a) Candidate A is declared the winner using the Borda count method. (b) The majority criterion is not satisfied. Candidate C has a majority of the first-place votes but Candidate C was not declared the winner of the election.

Work Step by Step

(a) With the Borda count method, each candidate receives 1 point for each fourth-place vote, 2 points for each third-place vote, 3 points for each second-place vote, and 4 points for each first-place vote. The candidate with the most points is declared the winner. We can find the total points for each candidate. Candidate A: 4(4) + 3(20 + 16) + 2(0) + 1(10) = 134 points Candidate B: 4(0) + 3(10 + 4) + 2(20 + 16) + 1(0) = 114 points Candidate C: 4(16 + 10) + 3(0) + 2(0) + 1(20 + 4) = 128 points Candidate D: 4(20) + 3(0) + 2(10 + 4) + 1(16) = 124 points Since Candidate A received the most points, Candidate A is declared the winner using the Borda count method. (b) The total number of votes in this election is 20 + 16 + 10 + 4 which is 50. Candidate C has 26 first-place votes which is more than half of the total votes in this election. Therefore, Candidate C has a majority of first-place votes. The majority criterion is not satisfied. Candidate C has a majority of the first-place votes but Candidate C was not declared the winner of the election.

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