924 CHAPTER 14 Voting and Apportionment Svetlana Foote/Shutterstock 14. Design of a Technology Building The planning committee of Tulsa Community College is considering three proposals, A, B, and C, for the design of a new technology building for the college. The eleven members of the planning committee rank the proposals according to the preference table shown below. Suppose that the Borda count method is used to determine the winner. Is the headto-head criterion satisfied? Explain. No. A is the winner by the Borda count method, but C is favored when compared to A and B. 17. Plurality: Irrelevant Alternatives Criterion Suppose that the plurality method is used on the following preference table. If B drops out, is the irrelevant alternatives criterion satisfied? Explain. No. A wins by the plurality method. If B drops out, C wins by the plurality method. Number of Votes 6 3 2 First C A B Second A B A Third B C C 15. A Taste Test Twenty-seven people are surveyed in the Mall of America and asked to taste and rank four different brands of chocolate ice cream. The following preference table shows the rankings of the 27 voters. Suppose that the plurality with elimination method is used to determine the winner. Is the head-to-head criterion satisfied? Explain. No. C wins by plurality with elimination, but B is favored over each of the other candidates using head-to-head comparisions. Number of Votes 11 3 5 8 First A B D C Second B C B B Third D A C A Fourth C D A D 16. Preference for Apple Pie Twenty-one people are asked to taste test and rank three different brands of apple pie. The following preference table shows the rankings of the 21 voters. Suppose that the plurality with elimination method is used to determine the winner. Is the head-tohead criterion satisfied? Explain. * Number of Votes 8 7 6 First B C A Second A A C Third C B B Number of Votes 10 5 6 First A C B Second C B C Third B A A 18. Plurality: Irrelevant Alternatives Criterion Suppose that the plurality method is used on the following preference table. If C drops out, is the irrelevant alternatives criterion satisfied? Explain. No. B wins by the plurality method. If C drops out, A wins by the plurality method. Number of Votes 7 5 4 First B C A Second C A C Third A B B 19. Borda Count: Irrelevant Alternatives Criterion Suppose that the Borda count method is used on the following preference table. If C drops out, is the irrelevant alternatives criterion satisfied? Explain. Yes. B wins by the Borda count method. If C drops out, B still wins. Number of Votes 10 9 8 First B C A Second A B C Third C A B 20. Borda Count: Irrelevant Alternatives Criterion Suppose that the Borda count method is used on the following preference table. If B drops out, is the irrelevant alternatives criterion satisfied? Explain. No. A wins by the Borda count method. If B drops out, C wins by the Borda count method. Number of Votes 7 6 5 First A C B Second B A C Third C B A *See Instructor Answer Appendix
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