Thinking Mathematically (6th Edition)

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

Chapter 13 - Voting and Apportionment - 13.2 Flaws of Voting Methods - Exercise Set 13.2: 1

Answer

(a) Design D has a majority of first-place votes. (b) Since Design A received the most points using the Borda count method, Design A will be used for the affordable housing. (c) The majority criterion is not satisfied.

Work Step by Step

(a) We can find the total number of votes in this election. votes = 300 + 120 + 90 + 60 = 570 Design D has 300 first-place votes which is more than half of the total votes in this election. Therefore, Design D has a majority of first-place votes. (b) With the Borda count method, each Design receives 1 point for each last place vote, 2 points for each second-to-last-place vote, and so on. The Design which receives the most points is declared the winner. We can find the total points for each design. Design A: 4(60) + 3(300 + 120 + 90) + 2(0) + 1(0) = 1770 points Design B: 4(0) + 3(0) + 2(300 + 120 + 60) + 1(90) = 1050 points Design C: 4(120 + 90) + 3(0) + 2(0) + 1(300 + 60) = 1200 points Design D: 4(300) + 3(60) + 2(90) + 1(120) = 1680 points Since Design A received the most points using the Borda count method, Design A will be used for the affordable housing. (c) The majority criterion is not satisfied. Design D has a majority of the first-place votes but Design D was not declared the winner of the election.
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