910 CHAPTER 14 Voting and Apportionment 14. Plurality Method Five candidates are running for president of the Student Senate. They receive the following votes: Michael 2192 Gerry 2562 Karen 1671 Felicia 2863 Stephen 1959 a) Determine the winner using the plurality method. Felicia b) Did this candidate receive a majority of votes? No Logo Choice In Exercises 15–20, members of the Tidewater Community College music club are choosing a new club logo. The choices are a guitar (G), a keyboard (K), and a musical note (N). Each member ranks the three choices from first to third. The following preference table shows the results of the ballots. 26. Determine the winner using the plurality with elimination method. Phoenix Number of Votes 9 5 3 2 First G K K N Second K G N K Third N N G G 15. How many members voted? 19 16. Is there a majority winner? No 17. Determine the winner using the plurality method. Guitar 18. Determine the winner using the Borda count method. Keyboard 19. Determine the winner using the plurality with elimination method. Keyboard 20. Determine the winner using the pairwise comparison method. Keyboard Choosing a Vacation Destination In Exercises 21–26, the Sanchez family is trying to decide whether to go to Denver (D), Washington, D.C. (W), or Phoenix (P) on their summer vacation. The parents, children, and grandparents rank their three choices according to the following preference table. Number of Votes 3 2 1 2 1 First D P D W P Second W D P P W Third P W W D D 21. How many family members voted? 9 22. Is there a majority winner? No 23. Determine the winner using the Borda count method. Denver 24. Determine the winner using the plurality method. Denver 25. Determine the winner using the pairwise comparison method. Three-way tie, no winner m Denver, CO NFL Expansion In Exercises 27–30, the National Football League (NFL) is considering four cities for expansion: San Antonio (S), Portland (P), Honolulu (H), and Toronto (T). The 32 current owners rank the four candidates according to the following preference table Number of Votes 8 6 3 4 3 3 2 1 2 First P S S H P H P T H Second S H P S S S H H P Third H T H T T P S P S Fourth T P T P H T T S T 27. Determine the winner using the plurality method. Portland 28. Determine the winner using the Borda count method. San Antonio 29. Determine the winner using the plurality with elimination method. No winner, a tie between Honolulu and Portland 30. Determine the winner using the pairwise comparison method. San Antonio Board of Trustees Election In Exercises 31–34, the 12 members of the executive committee of the Student Senate must vote for a student representative for the college board of trustees from among three candidates: Choi (C), Daniels (D), and Ross (R). The preference table follows. Number of Votes 5 1 4 2 First C D R R Second D R C D Third R C D C m Portland, OR Josemaria Toscano/123RF Roschetzky Photography/ Shutterstock
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