Explanation Given: A preference table. First Choice D B C A D Second Choice C C D C A Third Choice A D A B B Fourth Choice B A B D C Voters 39 32 27 21 12 a. Plurality method: In Plurality method, the candidate with the maximum first-place votes is the winner. In the table above, D is at the first place in columns 1 and 5. D has a total of 39+12=51 votes. Therefore, D has the maximum first-place votes and is the winner. So, the winner by plurality is D. b. Single runoff method: In Single runoff method, the two candidates with the most first-place votes face a runoff. The candidate who wins the runoff is the winner of the election. So, the runoff would be between first-place candidate D and second-place candidate B. Since, A and Care not there in the runoff, candidates who first chose A and C will now choose their second choice. If the second-choice is also A and C, they will select their third choice etc. All C’s voters have D as their second-choice, so D gets: 51+27=78 in the runoff. All A’s voters have C as their second-choice, so they will vote their third choice, that is, B. So, B gets: 32+15=53 votes. in the runoff. We see that D has more votes than B. So, the winner by single runoff is D. c. Sequential runoff method: In Sequential runoff method, a series of runoffs are conducted, where the candidate with the fewest first-place votes is eliminated at each stage. Runoffs go on till a candidate receives the majority of the first-place votes. In this case, A has the fewest first-place votes, so, A would be eliminated and a runoff would be there between first-place candidate D, second-place candidate B and third-place candidate C. Since, A is not there in the runoff, candidates who first chose A will now choose their second choice, that is, C. Therefore, C gets: 27+21=48 votes. Now, B has least first-place votes, so it will be eliminated and the runoff will be held between the first-place D candidate and the second-place candidate C. Since, B is not there in the runoff, candidates who first chose B will now choose their second choice, that is, C. Therefore, C gets: 48+32=80 votes. beating D’s 51 votes So, the winner by Sequential runoff is C. d. Point system (Bordacount) method: Points are given according to the rank of each candidate on the ballot. The candidate who gets the maximum points is the winner. In this case, we have 4 candidates. So, let’s give 4 points to the first place, 3 points to the second place, 2 points to the third place and 1 point to the fourth place. Received 21 first-choice, 12 second choice, (39+27)=66 third choices and 32 fourth choices...

6th Edition

ISBN: 8220100802713

Author: Briggs

Publisher: PEARSON

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Question

Chapter 12.A, Problem 30E

To determine

The winners for the preference table by plurality, single runoff, sequential runoff, point system and pairwise comparisons.

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Chapter 12.A, Problem 29E

Chapter 12.A, Problem 31E

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Chapter 12 Solutions

EBK USING AND UNDERSTANDING MATHEMATICS

Ch. 12.A - Prob. 1QQ Ch. 12.A - Prob. 2QQ Ch. 12.A - Prob. 3QQ Ch. 12.A - Prob. 4QQ Ch. 12.A - Prob. 5QQ Ch. 12.A - Prob. 6QQ Ch. 12.A - Prob. 7QQ Ch. 12.A - Prob. 8QQ Ch. 12.A - 9. Study Table 12.5. Which candidate received the...Ch. 12.A - 10. What is the primary lesson of the preference...

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