Thinking Mathematically (6th Edition)

Published by Pearson
ISBN 10: 0321867327
ISBN 13: 978-0-32186-732-2

Chapter 13 - Voting and Apportionment - Chapter Summary, Review, and Test - Review Exercises: 25

Answer

Using the plurality-with-elimination method, Candidate A wins the actual election. Originally, Candidate B won the straw vote. Then, 200 voters changed their vote in favor of Candidate B in the actual election. After this, Candidate B was not selected as the winner of the actual election. Therefore, the monotonicity criterion is not satisfied.

Work Step by Step

We can go through the plurality-with-elimination method again after 200 voters change their votes from C, B, A to B, C, A. With the plurality-with-elimination method, the candidate with the fewest number of first-place votes is eliminated in each round. After that candidate is eliminated, the other candidates ranked below that candidate on each ballot move up one spot. The rounds continue in this way until only one candidate remains, and this candidate is declared the winner. In round 1, we can count the number of first-place votes for each candidate. Candidate A: 400 Candidate B: 500 + 200 = 700 Candidate C: 350 In round 1, Candidate C has the fewest number of first-place votes, so Candidate C is eliminated. After Candidate C is eliminated, the other candidates ranked below Candidate C on each ballot move up one spot. In round 2, we can count the number of first-place votes for each candidate. Candidate A: 400 + 350 = 750 Candidate B: 500 + 200 = 700 In round 2, Candidate B has the fewest number of first-place votes, so Candidate B is eliminated. After Candidate B is eliminated, Candidate A is the only candidate remaining, so Candidate A is declared the winner. Using the plurality-with-elimination method, Candidate A wins the actual election. Originally, Candidate B won the straw vote. Then, 200 voters changed their vote in favor of Candidate B in the actual election. After this, Candidate B was not selected as the winner of the actual election. Therefore, the monotonicity criterion is not satisfied.
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