## Thinking Mathematically (6th Edition)

Published by Pearson

# Chapter 13 - Voting and Apportionment - Chapter 13 Test: 12

#### Answer

Candidate B is favored over all other candidates in head-to-head comparison. However, Candidate B was not declared the winner when using the plurality method. Therefore, the head-to-head criterion is not satisfied.

#### Work Step by Step

With a head-to-head comparison, each candidate is compared with every other candidate. For each pair of candidates, a candidate is favored over the other candidate if the candidate is ranked higher than the other candidate on a majority of ballots. We can compare Candidate A and Candidate B. Candidate A: 1500 Candidate B: 1000 + 1000 = 2000 Since Candidate B is ranked higher than Candidate A on more ballots, Candidate B is favored over Candidate A. We can compare Candidate A and Candidate C. Candidate A: 1500 + 1000 = 2500 Candidate C: 1000 Since Candidate A is ranked higher than Candidate C on more ballots, Candidate A is favored over Candidate C. We can compare Candidate B and Candidate C. Candidate B: 1500 + 1000 = 2500 Candidate C: 1000 Since Candidate B is ranked higher than Candidate C on more ballots, Candidate B is favored over Candidate C. We can see that Candidate B is favored over Candidate A and Candidate C. Therefore, Candidate B is favored over all other candidates in head-to-head comparison. Candidate B is favored over all other candidates in head-to-head comparison. However, Candidate B was not declared the winner when using the plurality method. Therefore, the head-to-head criterion is not satisfied.

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