Thinking Mathematically (6th Edition)

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

Chapter 13 - Voting and Apportionment - 13.1 Voting Methods - Exercise Set 13.1: 29

Answer

Soup B is declared the winner using the plurality-with-elimination method.

Work Step by Step

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 which were ranked below that candidate on each ballot move up one spot on that ballot. 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. Soup A: 34 Soup B: 30 Soup C: 6 Soup D: 2 In round 1, Soup D has the fewest number of first-place votes, so Soup D is eliminated. After Soup D is eliminated, the other candidates which were ranked below Soup D on each ballot move up one spot on that ballot. In round 2, we can count the number of first-place votes for each candidate. Soup A: 34 Soup B: 30 + 2 = 32 Soup C: 6 In round 2, Soup C has the fewest number of first-place votes, so Soup C is eliminated. After Soup C is eliminated, the other candidates which were ranked below Soup C on each ballot move up one spot on that ballot. In round 3, we can count the number of first-place votes for each candidate. Soup A: 34 Soup B: 30 + 2 + 6 = 38 In round 3, Soup A has the fewest number of first-place votes, so Soup A is eliminated. After Soup A is eliminated, Soup B is the only candidate remaining, so Soup B is declared the winner. Soup B is declared the winner using the plurality-with-elimination method.
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