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: 15

Answer

Comedy 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 ranked below that candidate on each ballot move up one spot. 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. comedy: 6 + 4 = 10 drama: 6 + 2 = 8 musical: 10 + 2 = 12 In round 1, drama has the fewest number of first-place votes, so drama is eliminated. After drama is eliminated, the other candidates ranked below drama on each ballot move up one spot. In round 2, we can count the number of first-place votes for each candidate. comedy: 6 + 6 + 4 = 16 musical: 10 + 2 + 2 = 14 In round 2, musical has the fewest number of first-place votes, so musical is eliminated. After musical is eliminated, comedy is the only candidate remaining, so comedy is declared the winner. Comedy is selected using the plurality-with-elimination method.
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