Thinking Mathematically (6th Edition)

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

Chapter 13 - Voting and Apportionment - Chapter 13 Test: 14

Answer

Candidate B is selected as the winner using the plurality-with-elimination method. Originally, Candidate C won the straw vote. Then, in the actual election, 30 voters changed their votes in favor of Candidate C. After this, Candidate C was not selected as the winner using the plurality-with-elimination method. Therefore, the monotonicity criterion is not satisfied.

Work Step by Step

After 30 voters change their votes from A, C, B to C, A, B, we can go through the plurality-with-elimination method again. 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: 50 Candidate B: 60 Candidate C: 70 + 30 = 100 In round 1, Candidate A has the fewest number of first-place votes, so Candidate A is eliminated. After Candidate A is eliminated, the other candidates ranked below Candidate A on each ballot move up one spot. In round 2, we can count the number of first-place votes for each candidate. Candidate B: 60 + 50 = 110 Candidate C: 70 + 30 = 100 In round 2, Candidate C has the fewest number of first-place votes, so Candidate C is eliminated. After Candidate C is eliminated, Candidate B is the only candidate remaining, so Candidate B is declared the winner. Candidate B is selected as the winner using the plurality-with-elimination method. Originally, Candidate C won the straw vote. Then in the actual election, 30 voters changed their votes in favor of Candidate C. After this, Candidate C was not selected as the winner using the plurality-with-elimination method. Therefore, the monotonicity criterion is not satisfied.
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