14.1 Voting Methods 909 Warm Up Exercises In Exercises 1–8, fill in the blank with an appropriate word, phrase, or symbol(s). 1. A candidate who receives more than 50% of the votes in an election is said to have a(n) ________ of votes. Majority 2. A table that summarizes the results of an election is called a(n) ________ table. Preference 3. When using the pairwise comparison method, the number of comparisons, c, needed when there are n candidates is determined by the formula c = ________. ( ) − n n 1 2 4. When there are four candidates, the number of comparisons needed with the pairwise comparison method is ________. 6 5. The voting method in which each voter votes for one candidate and the candidate receiving the most votes is declared the winner is called the ________ method. Plurality 6. In the Borda ________ voting method, the candidates are ranked from most favored to least favored. Count 7. The voting method in which each candidate is compared with each of the other candidates is called the pairwise ________ method. Comparison 8. The voting method that may involve a series of elections until a candidate receives a majority of the votes is called the ________ with elimination method. Plurality Practice the Skills/Problem Solving 9. Preference Table for Ice Cream Nine survey respondents are asked to rank three brands of ice cream: Ben & Jerry’s (B), Haagen-Dazs (H), and Dairy Queen (D). The nine survey respondents turn in the following ballots showing their preferences in order: First B D B H H H B D H SecondDBDBBDDHD Third HHHDDBHBB Exercises SECTION 14.1 10. Preference Table for Yogurt Eight voters are asked to rank three brands of yogurt: Delizioso (D), Baya (B), and Cremeux (C). The eight voters turn in the following ballots showing their preferences in order: First D C C B C B C D Second BDDDBDDB Third CBBCDCBC Make a preference table for these ballots. * 11. Energy Drinks Customers at a grocery store were asked to taste and rank three flavors of an energy drink: A, B, and C. Each voter ranks the three choices from first to third. The following preference table shows the results of the ranking. Number of Votes 15 7 5 3 First C B B A Second B C A B Third A A C C a) How many customers voted? 30 b) How many customers ranked the flavors in this order: B, C, A? 7 c) How many customers ranked B as their first choice? 12 12. Spaghetti Sauce Customers at a grocery store were asked to taste and rank four brands of spaghetti sauce: A, B, C, and D. Each voter ranks the four choices from first to fourth. The following preference table shows the results of the ranking. Number of Votes 11 8 3 2 First D B A A Second C C B B Third A A C D Fourth B D D C a) How many customers voted? 24 b) How many customers ranked the sauces in this order: B, C, A, D? 8 c) How many customers ranked A as their first choice? 5 13. Plurality Method Three candidates are running for mayor of Austin. They receive the following votes: Li 102,503 Sanchez 76,431 Johnson 91,863 a) Determine the winner using the plurality method. Li b) Did this candidate receive a majority of votes No *See Instructor Answer Appendix Make a preference table for these ballots. * Viki2win/Shutterstock
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