14.1 Voting Methods 905 several stages. One stage involves a variation of the plurality with elimination method in which the motion picture nominee with the fewest number of first-place votes is eliminated. Now we will discuss our next voting method, the pairwise comparison method. Pairwise Comparison Method To use the pairwise comparison method, each voter first ranks all the candidates. Then each candidate is compared with each of the other candidates using the rankings. It is treated like a round-robin tournament. For instance, if the candidates for an election were Bert, Ernie, and Louis, the following comparisons would be made: Bert versus Ernie, Bert versus Louis, and Ernie versus Louis. The winner of each individual comparison is awarded one point. If there is a tie, each candidate receives 1 2 point. The candidate who obtains the most points in the one-to-one comparisons is declared the winner. PAIRWISE COMPARISON METHOD 1. Voters rank the candidates. 2. A series of comparisons in which each candidate is compared with each of the other candidates follows. 3. If candidate A is preferred to candidate B, A receives 1 point. If candidate B is preferred to candidate A, B receives 1 point. If the candidates tie, each receives 1 2 point. 4. After making all comparisons among the candidates, the candidate receiving the most points is declared the winner. PROCEDURE Example 9 Selecting a Zoo Logo Using the Pairwise Comparison Method We will again examine the San Francisco Zoo logo election. Which animal is selected if the pairwise comparison method is used? Solution The preference table is shown again in Table 14.11. Recall that T stands for tiger, K stands for kangaroo, and G stands for giraffe. Table 14.11 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 To determine the winner, it is necessary to make comparisons between the tiger and the kangaroo, between the tiger and the giraffe, and between the kangaroo and the giraffe. We will begin by comparing the tiger and the kangaroo. We see from Table 14.11 that the 2 voters in the first column, the 3 voters in the second column, and the 5 voters in the third column all prefer the tiger to the kangaroo. We also see that the 1 voter in the fourth column, the 3 voters in the fifth column, and the 1 voter in the sixth column all prefer the kangaroo to the tiger. The pairwise comparison of the tiger versus the kangaroo is + + = + + = Tiger: 2 3 5 10 votes Kangaroo: 1 3 1 5 votes Timely Tip When we compared the tiger and the kangaroo in Example 9, we determined the sum of the tiger’s votes to be 10. Then we determined the sum of the kangaroo’s votes to be 5. Notice that 10 5 15, + = the number of votes in the preference table. If the tiger had 10 votes, the kangaroo must have 15–10 or 5 votes. When we use the pairwise comparison method, if you determine the number of votes of one member in the comparison, the number of votes of the second member can be determined by subtracting the first number of votes determined from the total number of votes. Ralph Loesche/Shutterstock
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