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: 17

Answer

Einstein is declared the new division chair 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. Darwin: 30 Einstein: 22 Freud: 20 Hawking: 12 + 2 = 14 In round 1, Hawking has the fewest number of first-place votes, so Hawking is eliminated. After Hawking is eliminated, the other candidates who were ranked below Hawking 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. Darwin: 30 Einstein: 22 + 12 = 34 Freud: 20 + 2 = 22 In round 2, Freud has the fewest number of first-place votes, so Freud is eliminated. After Freud is eliminated, the other candidates who were ranked below Freud 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. Darwin: 30 + 2 = 32 Einstein: 22 + 20 + 12 = 54 In round 3, Darwin has the fewest number of first-place votes, so Darwin is eliminated. After Darwin is eliminated, Einstein is the only candidate remaining, so Einstein is declared the winner. Einstein is declared the new division chair using the plurality-with-elimination method.
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