CHAPTER 14 Review Exercises 955 18. Using the plurality method, which plate is selected? American Music 19. Using the Borda count method, which plate is selected? American Music 20. Using the plurality with elimination method, which plate is selected? American Music 21. Using the pairwise comparison method, which plate is selected? American Music Accountants Convention In Exercises 22–26, The National Association of Accountants held an election among its delegates to decide on the 2025 conference site. The 200 delegates ranked their choices among Chicago (C), Seattle (S), Dallas (D), and Las Vegas (L). The preference table giving the results of the election is shown below. Number of Votes 60 55 45 30 10 First S L D C S Second L D C L D Third C C L D L Fourth D S S S C 22. Does any city receive a majority of first-place votes? If so, which city received a majority? No 23. Using the plurality method, which city is selected? Seattle 24. Using the Borda count method, which city is selected? Las Vegas 25. Using the plurality with elimination method, which city is selected? Las Vegas 26. Using the pairwise comparison method, which city is selected? Las Vegas Selecting a DVD Set In Exercises 27–29, Park Street Library is planning to invest in a set of children’s DVDs for the library, but the staff members differ regarding which set to buy. To settle the debate, the 16 staff members decide to rank the following choices: Chronicles of Narnia (C), Family Classic (F), Anne of Green Gables (A), and Where on Earth Is Carmen Sandiego? (W). Aware that sentiments seem to be evenly divided, the staff members agree to use the plurality with elimination method, with the Borda count method used in case of a tie. The results of this election are given in the following table. Number of Votes 6 4 3 1 1 1 First W C C F F W Second A A W W C F Third C W F A W C Fourth F F A C A A 27. Which DVD set is selected if the plurality with elimination method is used? A tie between Chronicles of Narnia and Where on Earth Is Carmen Sandiego? 28. According to the rules described above, which DVD set is chosen? Where on Earth Is Carmen Sandiego? 29. If the staff members had agreed to break a tie using the pairwise comparison method, which DVD set is chosen? A tie between Chronicles of Narnia and Where on Earth Is Carmen Sandiego? 14.2 Hiring a New Paralegal In Exercises 30 and 31, a law firm is hiring one new paralegal from among four candidates, A, B, C, and D. The search committee decides to use the Borda count method to determine the winner. The preference table follows. Number of Votes 10 7 2 First A C B Second B B D Third C D C Fourth D A A 30. Is the majority criterion satisfied? No. A has a majority, but B wins by the Borda count method. 31. Is the head-to-head criterion satisfied? * 32. Plurality with Elimination Consider the following preference table. Number of Votes 12 16 8 14 First B C B A Second A B C C Third C A A B a) Who wins the election if the plurality with elimination method is used? C wins the election by plurality with elimination. b) Assume that in a second election the eight voters who voted for B, C, A, in that order, all change their preference to C, B, A, in that order. If the plurality with elimination method is used, is the monotonicity criterion satisfied? When the order is changed, A wins. Therefore, the monotonicity criterion is not satisfied. c) Using the preference table from part (a), assume that B drops out. Does the plurality with elimination method satisfy the irrelevant alternatives criterion? * 33. A Taste Test In a taste test, 114 people are asked to taste and rank four different brands of spaghetti sauce. The choices are Ragu (R), Prego (P), Newman’s Own (N), and Barilla (B). The results of this taste test are given in the following preference table. *See Instructor Answer Appendix
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