14.2 Flaws of the Voting Methods 913 You are hosting a party and ask your guests to vote on whether they would like you to serve pizza, hot dogs, or hamburgers at the party. Each guest is asked to complete a ballot by ranking the three choices from most favorable to least favorable. You decide to use the Borda count method to determine the winner and announce that pizza wins. After reviewing the ballots, one of your friends quickly points out that hot dogs should win because a majority of voters ranked hot dogs as their first choice. This scenario suggests that there is a flaw with the Borda count method. In this section, we will discuss flaws with each of the voting methods introduced in Section 14.1. Flaws of the Voting Methods SECTION 14.2 LEARNING GOALS Upon completion of this section, you will be able to: 7 Determine if the results of an election violate the majority criterion. 7 Determine if the results of an election violate the head-tohead criterion. 7 Determine if the results of an election violate the monotonicity criterion. 7 Determine if the results of an election violate the irrelevant alternatives criterion. The board of directors of CSC Computers is using approval voting to fill two vacancies on their executive committee. Twenty-one ballots are cast as follows for candidates A, B, C, and D. a) Assume that the finishing positions are scored 4, 3, 2, 1 for first, second, third, and fourth place, respectively. How do the teams rank from highest to lowest if the Borda count method is used? Wildcats, Rams and Tigers tied, Comets b) Assume that the finishing positions are scored 5, 3, 1, 0 points for first, second, third, and fourth place, respectively. How do the teams rank from highest to lowest if we modify the Borda count method to use these values? Rams, Tigers, Wildcats, Comets 65. Using the Borda Count Method Suppose that 20 voters rank three candidates. a) What is the total number of points awarded to the candidates using the Borda count method? 120 b) Suppose that, using the Borda count method, candidate A receives 55 points and candidate C receives 25 points. How many points does candidate B receive? 40 c) Given the information from part (b), is it possible for candidate B to win an election if the Borda count method is used to determine the winner? Explain. No. Candidate A has more points than candidate B. 66. Using the Borda Count Method Suppose that 15 voters rank four candidates. a) What is the total number of points awarded to candidates using the Borda count method? 150 b) Suppose that using the Borda count method, candidate A receives 35 points, candidate B receives 40 points, and candidate C receives 25 points. How many points does candidate D receive? 50 c) Is it possible for candidate D to win? Explain. Yes 67. Using Approval Voting In many corporations and professional societies, the members of the board of directors are elected by a method called approval voting. With approval voting, a voter does not cast a ranked ballot. Instead, the voter votes for as many candidates as they would support. If a voter does not approve a candidate, they simply do not cast a vote for that candidate. The candidate(s) with the most votes wins. 1 2 3 4 5 6 7 8 9101112131415161718192021 A X X X X X X X X X X B X X X X X X X C X X X X X D X X X X X X X X X Using approval voting, which two candidates will win seats on the executive committee? A, D Research Activity 68. Award Methods Research and write a report on how voting is conducted on one of the following events: a) Academy Awards b) Grammy Awards c) Heisman Trophy Award d) Nobel Prizes e) Pulitzer Prize Include in your report how nominees are picked, who votes, how the voting takes place, and who tabulates the results. m Michelle Yeoh with her Academy Award John Angelillo/UPI/Shutterstock Shutterstock
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