14.1 Voting Methods 897 In this first section, we will describe four of the most popular voting methods and explain how they are implemented. In the next section, we will discuss the weaknesses and flaws of each method. We will discuss the following methods: 1. Plurality method 2. Borda count method 3. Plurality with elimination method 4. Pairwise comparison method Before we discuss any of these voting methods, though, we will illustrate how the results of an election might be indicated in a table called a preference table. A preference table summarizes the results of an election and shows how often each particular outcome was selected. In Example 1, we explain how to construct a preference table. Example 1 Balloting by Committee Members The planning committee for the San Francisco Zoo is voting on an animal for the new zoo logo. The choices are a tiger (T), a kangaroo (K), and a giraffe (G). There are 15 planning committee members (labeled CM1, CM2, CM3, . . ., CM15). Their ballots are shown in Fig. 14.1. Now try Exercise 9 CM1 1ST T 2ND K 3RD G CM2 1ST T 2ND G 3RD K CM3 1ST T 2ND K 3RD G CM4 1ST G 2ND T 3RD K CM5 1ST K 2ND G 3RD T CM6 1ST K 2ND T 3RD G CM7 1ST K 2ND T 3RD G CM8 1ST T 2ND G 3RD K CM9 1ST K 2ND T 3RD G CM10 1ST G 2ND T 3RD K CM11 1ST T 2ND G 3RD K CM12 1ST G 2ND T 3RD K CM13 1ST G 2ND T 3RD K CM14 1ST G 2ND T 3RD K CM15 1ST G 2ND K 3RD T Figure 14.1 Construct a preference table to illustrate the results of the election. Solution Notice that committee member 1 (CM1) listed T, K, G in that order. Also, notice that committee member 3 (CM3) also listed T, K, G, in that order. None of the other committee members listed this order of selection. Therefore, there are two committee members who listed T, K, G in that order. This information is indicated in the column in boldface in Table 14.2. Next look at CM2 who listed T, G, K in that order. Two other committee members, CM8 and CM11, also listed T, G, K in that order. Therefore, three committee members listed the order T, G, K. This information is indicated in the column to the right of the boldface column in Table 14.2. Continue this process to obtain the preference table. Table 14.2 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 Notice that the total number of votes indicated in the preference table is 15, which checks with the individual number of votes given. 7 Mark Malkinson/Alamy Stock Photo
RkJQdWJsaXNoZXIy NjM5ODQ=