14.2 Flaws of the Voting Methods 925 21. Plurality with Elimination: Monotonicity Criterion Suppose that the plurality with elimination method is used on the following preference table. If the four voters who voted A, C, B, in that order, change their vote to C, A, B, is the monotonicity criterion satisfied? Explain. * 25. Pairwise Comparison: Irrelevant Alternatives Criterion Suppose that the pairwise comparison method is used on the following preference table. If A, C, and E drop out, is the irrelevant alternatives criterion satisfied? Explain. * Number of Votes 7 8 4 10 First A B A C Second B C C A Third C A B B 22. Plurality with Elimination: Monotonicity Criterion Suppose that the plurality with elimination method is used on the following preference table. If the three voters who voted C, B, A, in that order, change their vote to B, C, A, is the monotonicity criterion satisfied? Explain. * Number of Votes 5 6 3 7 First C A C B Second A B B C Third B C A A 23. Pairwise Comparison Method: Monotonicity Criterion Suppose that the pairwise comparison method is used on the following preference table. If the five voters who voted C, D, A, B, in that order, change their votes to D, C, A, B, is the monotonicity criterion satisfied? Explain. * Number of Votes 8 7 6 5 First D B B C Second C A A D Third A C D A Fourth B D C B 24. Borda Count: Monotonicity Criterion Suppose that the Borda count method is used on the following preference table. If the three voters who voted C, A, D, B, in that order, change their votes to A, C, D, B, is the monotonicity criterion satisfied? Explain. * Number of Votes 8 7 5 3 First A B D C Second B D A A Third C C C D Fourth D A B B Number of Votes 1 1 1 1 1 First B B A C E Second A C D D D Third C E B B B Fourth E A C E A Fifth D D E A C 26. Pairwise Comparison: Irrelevant Alternatives Criterion Suppose that the pairwise comparison method is used on the following preference table. If A, B, and E drop out, is the irrelevant alternatives criterion satisfied? Explain. No. C wins by pairwise comparison. If A, B, and E drop out, D wins by pairwise comparison. Number of Votes 2 1 1 1 1 1 First C C D A E B Second E B C D A E Third A A B C D D Fourth B E A B C C Fifth D D E E B A 27. Borda Count: Majority Criterion Suppose that the Borda count method is used on the following preference table. Is the majority criterion satisfied? No. B wins by the Borda count method, but A has a majority of first-place votes. Number of Votes 5 3 1 First A B C Second B C B Third C A A 28. Borda Count: Majority Criterion Suppose that the Borda count method is used on the following preference table. Is the majority criterion satisfied? No. C wins by the Borda count method, but B has a majority of first-place votes. Number of Votes 5 1 4 1 First B B C A Second C A A C Third A C B B *See Instructor Answer Appendix
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