898 CHAPTER 14 Voting and Apportionment When an election has many voters, a preference table is an efficient way to report the results. The initial purpose of Example 1 was to introduce the preference table. We will revisit the zoo logo election several times in this section. Example 2 introduces another election that will be used frequently in this section. Example 2 Voting for the Veterans Club President Four students are running for president of the Maricopa Community College Veterans Club: Antoine (A), Betty (B), Carlos (C), and Don (D). The club members were asked to rank all candidates. The resulting preference table for this election is given in Table 14.3. Now try Exercise 11 Table 14.3 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 a) How many students voted in the election? b) How many students ranked the candidates in this order: C, A, D, B? c) How many students ranked C as their first choice? Solution a) To determine the number of students who voted, we add the numbers in the row labeled Number of Votes. 19151172 54 + + + + = Therefore, 54 students voted in the election. b) Fifteen students (the second column from the left) ranked the candidates in the order C, A, D, B. c) To determine the number of voters who ranked C as their first choice, read across the row that says First. When you see a C in the row, record the number above it. Then determine the sum of the numbers. Thus, 15 2 17 students ranked C as their first choice. + = 7 Now we will begin to examine the results of the elections in Examples 1 and 2. Each election will be analyzed using each of the four different voting methods to be discussed in this section: plurality method, Borda count method, plurality with elimination method, and pairwise comparison method. Plurality Method When electing a candidate using the plurality method, each voter votes for only one candidate. The candidate receiving the most votes is declared the winner. With the plurality method, a preference table does not have to be used, since the candidates are not ranked. In this section, we will often use a preference table, since the data may often be given in that form from a previous example. The plurality method is the most commonly used method, and it is the easiest method to use when there are more than two candidates. Carlofranco/E+/Getty Images
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