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: 23

Answer

Candidate A has a majority of first-place votes, but it is not selected as the winner when using the Borda count method. Therefore, the Borda count method violates the majority criterion in this election.

Work Step by Step

Candidate A has 180 first-place votes, which is more than half the votes. Therefore, Candidate A has a majority of first-place votes. Candidate A is selected as the winner using the plurality method. Using the Borda count method, Candidate B wins the election. Candidate A is selected as the winner using the plurality-with-elimination method. Candidate A wins the election using the pairwise comparison method. Candidate A has a majority of first-place votes, but it is not selected as the winner when using the Borda count method. Therefore, the Borda count method violates the majority criterion in this election.
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