Explanation Given: The election data given in the following table: Number of Votes 36 20 8 6 First A B C D Second B C B B Third D A D A Fourth C D A C Voting method use: Borda count voting method: 1. Voters rank the candidates from the most favorable to the least favorable. 2. Each last place vote is rewarded one point, each next to last place vote is rewarded two points, each third place from the last place is rewarded three points, and so forth. 3. The candidate receiving the most points is the winner of the election. Calculation: The majority out of 70 votes is 36 or more votes. The candidate A has 36 first-place votes (more than 50% of total votes) and declared the winner using the majority criterion. Now, need to check which method violates the majority criterion. According to the steps of Borda count method, in this problem there are four choices A, B, C, and D. So a first place vote is worth 4 points, a second place vote is worth 3 points, a third place vote is worth 2 point and a fourth place vote worth 1. Use preference table to obtain the total award points of candidate A, The 36 first- place votes produce 36 × 4 = 144 points. Similarly, the 0 second- place votes produce 0 × 3 = 0 points. The sum 20 + 6 = 26 third-place votes produce 26 × 2 = 52 points and the 8 fourth- place votes produce 8 × 1 = 8 points. Thus, the candidate A receives 144 + 52 + 8 = 204 points. Similarly, obtain the total award points of the candidate B, The 20 first- place votes gives 20 × 4 = 80 points. The sum 36 + 8 + 6 = 50 second-place votes gives 50 × 3 = 150 points. Similarly, the 0 third- place votes gives 0 × 2 = 0 points and the 0 fourth- place votes gives 0 × 1 = 0 points

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Chapter 14, Problem 25RE

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Which voting method(s) violates the majority criterion.

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Chapter 14 Solutions

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Which voting method(s) violates the majority criterion.

Solution Summary: The author explains how the Borda count voting method violates the majority criterion. The candidate receiving the most points is the winner of the election.

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