Thinking Mathematically (6th Edition)

Published by Pearson
ISBN 10: 0321867327
ISBN 13: 978-0-32186-732-2

Chapter 13 - Voting and Apportionment - Chapter Summary, Review, and Test - Review Exercises: 29

Answer

Before Candidate C drops out, Candidate B was selected as the winner using the Borda count method. After one of the losing candidates, Candidate C, drops out, Candidate B was again selected as the winner using the Borda count method. Therefore, the irrelevant alternatives criterion is satisfied.

Work Step by Step

With the Borda count method, each candidate receives 1 point for each last place vote, 2 points for each second-to-last-place vote, and so on. The candidate with the most points is declared the winner. We can find the total points for each candidate before Candidate C drops out. Candidate A: 3(400) + 2(0) + 1(250 + 200) = 1650 points Candidate B: 3(200) + 2(400 + 250) + 1(0) = 1900 points Candidate C: 3(250) + 2(200) + 1(400) = 1550 points Since Candidate B received the most points using the Borda count method, Candidate B wins the election. After Candidate C drops out, we can go through the Borda count method again. Note that every candidate below Candidate C on a ballot moves up one spot on that ballot. We can find the total points for each candidate. Candidate A: 2(400) + 1(250 + 200) = 1250 points Candidate B: 2(250 + 200) + 1(400) = 1300 points Since Candidate B received the most points using the Borda count method, Candidate B wins the election. Before Candidate C drops out, Candidate B was selected as the winner using the Borda count method. After one of the losing candidates, Candidate C, drops out, Candidate B was again selected as the winner using the Borda count method. Therefore, the irrelevant alternatives criterion is satisfied.
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