Explanation Given: Preference table of first election: Number of Votes 28 24 20 10 First A B C C Second C A B A Third B C A B Preference table of second election: Number of Votes 36 24 20 2 First A B C C Second C A B A Third B C A B Voting method use: Plurality-with-elimination: 1. Each voter votes for one candidate. 2. If a candidate receives a majority of votes, that candidate is declared the winner of the election. 3. If no candidate receives a majority, eliminate the candidate with the fewest votes and hold another election (if there is a tie for the fewest votes, eliminate all candidates tied for the fewest votes). 4. Repeat this process until a candidate receives a majority. Calculation: Given that the total number of votes is 82, means that the majority out of 82 votes is 42 or more votes. Now, first count the number of first place votes for each candidate for first election. The first place votes for A are equal to 28, for B is equal to 24, and for C is equal to 30. That is, there are out of 82 votes 42 or more votes are needed to receive a majority. In this election no candidate out of three received a majority of votes. Since the candidate B received the fewest number of first- place votes (24 votes only), and eliminated in the first round. Now, assume that the all preference orders remain the same. The election preference table after the candidate B is eliminated. Number of Votes 36 24 20 2 First A A C C Second C C A A From the second preference table, it is noticed that the first place votes for A is 60 and for the C is 22

A Survey of Mathematics with Applications (10th Edition) - Standalone book

10th Edition

ISBN: 9780134112107

Author: Allen R. Angel, Christine D. Abbott, Dennis Runde

Publisher: PEARSON

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Chapter 14, Problem 26RE

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Which voting method(s) violates the monotonicity criterion.

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Chapter 14 Solutions

A Survey of Mathematics with Applications (10th Edition) - Standalone book

Ch. 14.1 - In Exercise 1-8, fill in the blank with an...Ch. 14.1 - In Exercise 1-8, fill in the blank with an...Ch. 14.1 - In Exercise 1-8, fill in the blank with an...Ch. 14.1 - In Exercise 1-8, fill in the blank with an...Ch. 14.1 - Prob. 5E Ch. 14.1 - In Exercise 1-8, fill in the blank with an...Ch. 14.1 - Prob. 7E Ch. 14.1 - Prob. 8E Ch. 14.1 - Plurality Three candidates are running for mayor...Ch. 14.1 - Prob. 10E

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Which voting method(s) violates the monotonicity criterion.

Solution Summary: The author explains how the plurality-with-elimination method violates the monotonicity criterion.

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Which voting method(s) violates the monotonicity criterion.

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