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: 34

Answer

Sweeney Todd is selected 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. Cabaret: 5 + 4 = 9 The Producers: 2 Rent: 0 Sweeney Todd: 5 West Side Story: 3 + 3 = 6 In round 1, Rent has the fewest number of first-place votes, so Rent is eliminated. After Rent is eliminated, the other candidates which were ranked below Rent 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. Cabaret: 5 + 4 = 9 The Producers: 2 Sweeney Todd: 5 West Side Story: 3 + 3 = 6 In round 2, The Producers has the fewest number of first-place votes, so The Producers is eliminated. After The Producers is eliminated, the other candidates which were ranked below The Producers 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. Cabaret: 5 + 4 = 9 Sweeney Todd: 5 + 2 = 7 West Side Story: 3 + 3 = 6 In round 3, West Side Story has the fewest number of first-place votes, so West Side Story is eliminated. After West Side Story is eliminated, the other candidates which were ranked below West Side Story on each ballot move up one spot on that ballot. In round 4, we can count the number of first-place votes for each candidate. Cabaret: 5 + 4 = 9 Sweeney Todd: 5 + 2 + 3 + 3 = 13 In round 4, Cabaret has the fewest number of first-place votes, so Cabaret is eliminated. After Cabaret is eliminated, Sweeney Todd is the only candidate remaining, so Sweeney Todd is declared the winner. Sweeney Todd is selected using the plurality-with-elimination method.
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