Thinking Mathematically (6th Edition)

Published by Pearson

Chapter 13 - Voting and Apportionment - 13.1 Voting Methods - Exercise Set 13.1: 16

Answer

New York 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. New York: 8 + 6 = 14 Chicago: 4 San Francisco: 16 In round 1, Chicago has the fewest number of first-place votes, so Chicago is eliminated. After Chicago is eliminated, the other candidates ranked below Chicago on each ballot move up one spot. In round 2, we can count the number of first-place votes for each candidate. New York: 8 + 6 + 4 = 18 San Francisco: 16 In round 2, San Francisco has the fewest number of first-place votes, so San Francisco is eliminated. After San Francisco is eliminated, New York is the only candidate remaining, so New York is declared the winner. New York is selected using the plurality-with-elimination method.

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