Thinking Mathematically (6th Edition)

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

Chapter 13 - Voting and Apportionment - 13.1 Voting Methods - Exercise Set 13.1: 23

Answer

Comedy is selected 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 comedy and drama. We can find the number of ballots with comedy ranked higher than drama, and the number of ballots with drama ranked higher than comedy. comedy: 10 + 6 + 4 = 20 drama: 6 + 2 + 2 = 10 Since comedy is ranked higher than drama on more ballots, comedy receives 1 point. We can compare comedy and musical. We can find the number of ballots with comedy ranked higher than musical, and the number of ballots with musical ranked higher than comedy. comedy: 6 + 6 + 4 = 16 musical: 10 + 2 + 2 = 14 Since comedy is ranked higher than musical on more ballots, comedy receives 1 point. We can compare musical and drama. We can find the number of ballots with musical ranked higher than drama, and the number of ballots with drama ranked higher than musical. musical: 10 + 6 + 2 = 18 drama: 6 + 4 + 2 = 12 Since musical is ranked higher than drama on more ballots, musical receives 1 point. After all the pairwise comparisons have been made, we can add up the total number of points for each candidate. drama: 0 points comedy: 1 + 1 = 2 points musical: 1 point Since comedy received the most points, comedy is declared the winner. Comedy is selected using the pairwise comparison method.
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