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 889: 27

Answer

Originally, when there were three candidates, Candidate A was selected as the winner using the plurality method. After a losing candidate, Candidate B, drops out, Candidate A is not selected as the winner using the plurality method. Therefore, the irrelevant alternatives criterion is not satisfied.
1515637407

Work Step by Step

When there were three candidates, Candidate A was selected as the winner using the plurality method, because Candidate A had the highest number of first-place votes in the original preference table. We can see the preference table below after Candidate B drops out. Note that every other candidate below Candidate B on a ballot moves up one spot on that ballot after Candidate B drops out. With the plurality method, the candidate with the highest number of first-place votes is selected as the winner. We can find the number of first-place votes for each candidate. Candidate A: 400 Candidate C: 250 + 200 = 450 Since Candidate C has the highest number of first-place votes, Candidate C is selected as the winner using the plurality method. Originally, when there were three candidates, Candidate A was selected as the winner using the plurality method. After a losing candidate, Candidate B, drops out, Candidate A is not selected as the winner using the plurality method. Therefore, the irrelevant alternatives criterion is not satisfied.
Small 1515637407
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.