Thinking Mathematically (6th Edition)

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

Chapter 13 - Voting and Apportionment - Chapter Summary, Review, and Test - Review Exercises - Page 888: 16

Answer

Design A is favored over all other designs using a head-to-head comparison, but it is not selected as the winner using the Borda count method. Therefore, the head-to-head criterion is not satisfied.

Work Step by Step

Design A has 1500 first-place votes, which is more than half the votes. Therefore, Design A has a majority of first-place votes. Since Design A has a majority of first-place votes, Design A is favored over all other designs when we compare them head-to-head. However, using the Borda count method, Design B is selected as the winning design. Design A is favored over all other designs using a head-to-head comparison, but it is not selected as the winner using the Borda count method. Therefore, the head-to-head criterion is not satisfied.
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