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: 15

Answer

Originally Candidate B was selected as the winner. After one of the losing candidates, Candidate C, drops out, Candidate B is not selected as the winner. Therefore, the irrelevant alternatives criterion is not satisfied.

Work Step by Step

With the plurality method, the candidate with the highest number of first-place votes is selected as the winner. We can find the number of first-place votes for each candidate. Candidate A: 45 Candidate B: 90 Candidate C: 75 Since Candidate B has the highest number of first-place votes, Candidate B is selected as the winner using the plurality method. After Candidate C drops out, we can go through the plurality method again. Note that every other candidate below Candidate C on a ballot moves up one spot on that ballot. We can find the number of first-place votes for each candidate. Candidate A: 45 + 75 = 120 Candidate B: 90 Since Candidate A has the highest number of first-place votes, Candidate A is selected as the winner using the plurality method. Originally, Candidate B was selected as the winner. After one of the losing candidates, Candidate C, drops out, Candidate B is not selected as the winner. Therefore, the irrelevant alternatives criterion is not satisfied.
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