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: 37

Answer

Since the plurality method leads to a tie, we need to use the Borda count method. Candidate C is declared the new mayor using the Borda count method.

Work Step by Step

Using the plurality method, the candidate who has the most first-place votes is declared the winner of the election. We can find the number of first-place votes for each candidate. The number of first-place votes for Candidate A is 7500 + 4500 which is 12,000. The number of first-place votes for Candidate B is 0. The number of first-place votes for Candidate C is 12,000. Candidate A and Candidate C are tied with 12,000 first-place votes. Since the plurality method leads to a tie, we need to use the Borda count method. With the Borda count method, each candidate receives 1 point for each third-place vote, 2 points for each second-place vote, and 3 points for each first-place vote. The candidate who receives the most points is declared the winner. We can find the total points for each candidate. Candidate A: 3(7500 + 4500) + 2(0) + 1(12,000) = 48,000 points Candidate B: 3(0) + 2(12,000 + 7500) + 1(4500) = 43,500 points Candidate C: 3(12,000) + 2(4500) + 1(7500) = 52,500 points Since Candidate C received the most points, Candidate C is declared the new mayor using the Borda count method.
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