926 CHAPTER 14 Voting and Apportionment 29. Spring Trip The Quilting Club of Charlotte is voting on which city to visit for its spring trip. The choices are Chicago (C), Savannah (S), Philadelphia (P), and Boston (B). The preference table for the 23 members’ choices is given below. m Philadelphia, PA e) Which company is selected using the pairwise comparison method? A f) For this preference table, which voting method(s), if any, violate the majority criterion? Borda count 31. Selecting a Spokesperson The Campbell Soup Company is selecting a new spokesperson for its advertisements. The choices are Will Ferrell (F), Michael B. Jordan (J), and Serena Williams (W). At the annual meeting of its managers, a straw vote is taken to gauge the managers’ initial reaction to the candidates. The results of this straw vote are given in the preference table below. Number of Votes 12 8 3 First S P B Second C C S Third P B P Fourth B S C a) Which city, if any, holds a majority of first-place votes? Savannah b) Which city is selected using the plurality method? Savannah c) Which city is selected using the Borda count method? Savannah d) Which city is selected using the plurality with elimination method? Savannah e) Which city is selected using the pairwise comparison method? Savannah f) For this preference table, which voting method(s), if any, violate the majority criterion? None of them 30. Investment Choices The Motley Crew Investing Club wishes to purchase stock in a pharmaceutical company. The choices are American Pharmacy (A), BurrowsWelcome (B), and Chicago Labs (C). The choice rankings are shown in the following preference table. Number of Votes 15 10 3 First A B C Second B C B Third C A A a) Which company, if any, holds a majority of first place votes? A b) Which company is selected using the plurality method? A c) Which company is selected using the Borda count method? B d) Which company is selected using the plurality with elimination method? A Number of Votes 28 24 20 10 First W J F F Second F W J W Third J F W J m Serena Williams After discussion about the candidates, eight people who had supported Will Ferrell over Serena Williams now switch their preferences to Serena Williams over Will Ferrell. This switch leads to the following preference table. Number of Votes 36 24 20 2 First W J F F Second F W J W Third J F W J a) Using the plurality with elimination method, which person is selected from the first (or straw) vote? Serena Williams b) Using the plurality with elimination method, which person is selected from the second vote? Michael B. Jordan c) Does this second result violate the monotonicity criterion? Yes Sean Pavone/Shutterstock Anatoliy Lukich/Shutterstock
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