## Thinking Mathematically (6th Edition)

Published by Pearson

# 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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