954 CHAPTER 14 Voting and Apportionment 14.1 1. Electing the Club President The Sailing Club of Lakeport is holding an election to choose the club president. The 42 votes were cast as follows: Comstock, 20 votes; Pendergast, 15 votes; and Hanzalik, 7 votes. a) Using the plurality method, which candidate is elected president? Comstock b) Did this candidate receive a majority of votes? No 2. Electing a Chairperson Suffolk County Community College is holding an election to appoint a chairperson of the board of trustees. The 413 faculty members vote as follows: Michelle, 231 votes; Jeffrey, 155 votes; and Donald, 27 votes. a) Using the plurality method, who is elected? Michelle b) Did this candidate receive a majority of votes? Yes 3. Ranking Candidates Ten voters are asked to rank four candidates. The 10 voters turn in the following ballots showing their preferences in order: BADBACBCDC ACCACBABAB CDACDACABA DBBDBDDDCD Make a preference table for these ballots. * 4. Ranking Candidates Seven voters are asked to rank three candidates. The seven voters turn in the following ballots showing their preferences in order: C C A C A B B A A C B C A A B B B A B C C Make a preference table for these ballots. * Student Council In Exercises 5–10, the members of the Student Council at Louisiana State University are planning to go out to dinner following an upcoming meeting. The restaurant choices are Chipotle Mexican Grill (C), Jimmy John’s (J), Domino’s Pizza (D), and Burger King (B). The members rank their choices according to the following preference table. Number of Votes 5 3 1 2 First C D D B Second D B B C Third B J C J Fourth J C J D 5. How many members voted? 11 6. Using the plurality method, which restaurant is chosen? Chipotle Mexican Grill Review Exercises CHAPTER 14 7. Using the Borda count method, which restaurant is chosen? Domino’s Pizza 8. Using the plurality with elimination method, which restaurant is chosen? Chipotle Mexican Grill 9. Using the pairwise comparison method, which restaurant is chosen? Three-way tie, no winner 10. Which restaurant is chosen if the plurality with elimination method is used and the restaurant with the most last-place votes is eliminated at each step? Chipotle Mexican Grill Sports Preferences In Exercises 11–16, the employees at Delphi Engineering must decide whether to play baseball (B), soccer (S), or volleyball (V) at their year-end picnic. The preference table follows. Number of Votes 38 30 25 7 10 First S V B B V Second B S V S B Third V B S V S 11. How many employees voted? 110 12. Determine the winner using the plurality method. Volleyball 13. Determine the winner using the Borda count method. Soccer 14. Determine the winner using the plurality with elimination method. Volleyball 15. Determine the winner using the pairwise comparison method. None, a three-way tie 16. Determine the winner if the plurality with elimination method is used and the candidate with the most last-place votes is eliminated at each step. Soccer Choosing a License Plate Style In Exercises 17–21, Park Forest retirement community in Tennessee is purchasing a van to be used by the residents. The 372 residents are unable to agree on a style of license plate for the van and decide to hold an election in which the residents rank their choices from among the following: American Music (A), standard issue Tennessee license plate (T), Wildlife (W), and State Parks (S). The results of this election are given in the preference table below. Number of Votes 161 134 65 12 First A A T W Second S W A S Third T S W T Fourth W T S A 17. Does any plate receive a majority of first-place votes? If so, which plate received a majority? Yes, American Music *See Instructor Answer Appendix
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