14.1 Voting Methods 901 Example 6 Electing the Veterans Club President Using the Borda Count Method Use the Borda count method to determine the winner of the election for president of the Veterans Club discussed in Example 2. Recall that the candidates are Antoine (A), Betty (B), Carlos (C), and Don (D). For convenience, the preference table is reproduced below in Table 14.5. Now try Exercise 31 Table 14.5 Veterans Club Preference Table Number of Votes 19 15 11 7 2 First B C D A C Second A A C D D Third C D A C A Fourth D B B B B Solution In this problem, there are four candidates, so a first-place vote is worth 4 points, a second-place vote is worth 3 points, a third-place vote is worth 2 points, and a fourth-place vote is worth 1 point. Using Table 14.5, we see that: Antoine receives × = + = × = + = × = 7 7 34 34 13 13 first-place votes producing 4 28 points, 19 15 second-place votes producing 3 102 points, and 11 2 third-place votes producing 2 26points Antoine has no fourth-place votes. Therefore, Antoine receives 28 102 26 + + = 156 points. Betty receives × = + + + = × = 19 19 35 35 first-place votes producing 4 76 points, and 15 11 7 2 fourth-place votes producing 1 35points Betty has no second- or third-place votes. Therefore, Betty receives 76 35 + = 111 points. Carlos receives + = × = × = + = × = 17 17 11 11 26 15 2 first-place votes producing 4 68 points, second-place votes producing 3 33 points, and 19 7 26 third-place votes producing 2 52points Carlos has no fourth-place votes. Therefore, Carlos receives 68 33 52 + + = 153 points. Don receives × = + × = × = × = 11 11 9 9 15 15 19 19 first-place votes producing 4 44 points, 7 2 = second-place votes producing 3 27 points, third-place votes producing 2 30 points, and fourth-place votes producing 1 19 points Therefore, Don receives 44 27 30 19 120 points. + + + = Antoine, with 156 points, receives the most points using the Borda count method and is declared the winner. 7 Borda Count Method
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