Thinking Mathematically (6th Edition)

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

Chapter 13 - Voting and Apportionment - Chapter 13 Test: 8

Answer

Candidate A is declared the winner using the pairwise comparison method.

Work Step by Step

With the pairwise comparison method, each candidate is compared with every other candidate. For each pair of candidates, if one candidate is ranked higher than the other candidate on a majority of ballots, then the higher-ranked candidate receives 1 point. If the two candidates tie, then they each receive 0.5 points. After all the comparisons have been made, the candidate who receives the most points is declared the winner. We can compare Candidate A and Candidate C. We can find the number of ballots with Candidate A ranked higher than Candidate C and the number of ballots with Candidate C ranked higher than Candidate A. Candidate A: 1200 + 600 = 1800 Candidate C: 900 + 900 = 1800 Since they tie, both candidates receive 0.5 points. We can compare Candidate A and Candidate B. We can find the number of ballots with Candidate A ranked higher than Candidate B and the number of ballots with Candidate B ranked higher than Candidate A. Candidate A: 1200 + 900 = 2100 Candidate B: 900 + 600 = 1500 Since Candidate A is ranked higher than Candidate B on more ballots, Candidate A receives 1 point. We can compare Candidate B and Candidate C. We can find the number of ballots with Candidate B ranked higher than Candidate C and the number of ballots with Candidate C ranked higher than Candidate B. Candidate B: 1200 + 900 + 600 = 2700 Candidate C: 900 Since Candidate B is ranked higher than Candidate C on more ballots, Candidate B receives 1 point. After all of the pairwise comparisons have been made, we can add up the total number of points for each candidate. Candidate A: 1 + 0.5 = 1.5 points Candidate B: 1 point Candidate C: 0.5 points Since Candidate A received the most points, Candidate A is declared the winner. Candidate A is declared the winner using the pairwise comparison method.
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