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: 18

Answer

Sarnoff is declared the new president 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 who 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. Disney: 10 Ford: 30 Gates: 22 + 2 = 24 Sarnoff: 18 In round 1, Disney has the fewest number of first-place votes, so Disney is eliminated. After Disney is eliminated, the other candidates who were ranked below Disney 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. Ford: 30 Gates: 22 + 2 = 24 Sarnoff: 18 +10 = 28 In round 2, Gates has the fewest number of first-place votes, so Gates is eliminated. After Gates is eliminated, the other candidates who were ranked below Gates 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. Ford: 30 Sarnoff: 22 + 18 + 10 + 2 = 52 In round 3, Ford has the fewest number of first-place votes, so Ford is eliminated. After Ford is eliminated, Sarnoff is the only candidate remaining, so Sarnoff is declared the winner. Sarnoff is declared the new president using the plurality-with-elimination method.
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