900 CHAPTER 14 Voting and Apportionment We will now reexamine the election for president of the Veterans Club by using the Borda count method. The primary advantage of the Borda count method is that voters are able to provide more information than in the plurality method. Many well-known ranking systems use variations of the Borda count method. The Heisman trophy, given annually to the best college football player, is awarded by having the voters (sportswriters and former Heisman trophy winners) rank their first, second, and third choices out of possibly thousands of college football players. A player receives 3 points for each firstplace vote, 2 points for each second-place vote, and 1 point for each third-place vote. Profile in Mathematics Jean-Charles de Borda Jean-Charles de Borda (1733– 1799), a French calvary officer and naval captain for whom the Borda count method is named, wrote on a variety of subjects, including mathematics, physics, design of scientific experiments, and voting theory. Example 5 Selecting a Zoo Logo Using the Borda Count Method Let’s reexamine the San Francisco Zoo election for a new logo as discussed in Example 1. For convenience, the preference table is reproduced in Table 14.4. Recall that T represents tiger, K represents kangaroo, and G represents giraffe. Which animal is selected using the Borda count method? Now try Exercise 23 Table 14.4 San Francisco Zoo Logo Preference Table Number of Votes 2 3 5 1 3 1 First T T G K K G Second K G T G T K Third G K K T G T Solution In this problem, there are three candidates, so a first-place vote is worth 3 points, a second-place vote is worth 2 points, and a third-place vote is worth 1 point. To award points, we examine each candidate starting with the tiger. Using Table 14.4, we see that the Tiger receives 5 5 8 8 2 2 2 3 first-place votes producing 3 15 points, 5 3 second-place votes producing 2 16 points, and 1 1 third-place votes producing 1 2 points + = × = + = × = + = × = Therefore, the tiger receives 15 16 2 33 points. + + = Giraffe receives 6 6 4 4 5 5 5 1 first-place votes producing 3 18 points, 3 1 second-place votes producing 2 8 points, and 2 3 third-place votes producing 1 5 points + = × = + = × = + = × = Therefore, the giraffe receives 18 8 5 31 points. + + = Kangaroo receives 4 4 3 3 8 8 1 3 first-place votes producing 3 12 points, 2 1 second-place votes producing 2 6 points, and 3 5 third-place votes producing 1 8 points + = × = + = × = + = × = Therefore, the kangaroo receives 12 6 8 26 + + = points. The tiger receives 33 points, the giraffe receives 31 points, and the kangaroo receives 26 points. By using the Borda count method, the tiger is chosen for the zoo logo. 7 Learning Catalytics Keyword: Angel-SOM-14.1 (See Preface for additional details.)
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