14.1 Voting Methods 903 We see now that the tiger has 2 3 3 8 + + = first-place votes and the giraffe has 5 1 1 7 + + = first-place votes. The tiger has eight of 15 first-place votes, a majority. Using the plurality with elimination method, the tiger is chosen for the zoo logo. 7 Solution Reexamine the preference table shown in Table 14.6. Now try Exercise 19 Table 14.6 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 We first count the number of first-place votes for each animal: + = + = + = Tiger: 2 3 5 Giraffe: 5 1 6 Kangaroo: 1 3 4 To receive a majority, a candidate must have more than half of the votes. Since there are 15 people voting, 8 or more votes are needed to receive a majority. In this election, no candidate received a majority. Since the kangaroo received the fewest number of first-place votes, it is eliminated in the first round. Next, we assume that all preference orders remain the same. For example, the three committee members who had their preference order of K, T, and G will now have a preference order of T and G. Table 14.7 shows the new preference table after the kangaroo is eliminated. Table 14.7 Zoo Logo Preference Table After the Kangaroo Is Eliminated Number of Votes 2 3 5 1 3 1 First T T G G T G Second G G T T G T Did You Know Ranked Choice Voting gains popularity A voting method similar to plurality with elimination, that is gaining popularity, is ranked choice voting (RCV). RCV is also called instant runoff voting or preferential voting . The difference between RCV and plurality with elimination is that RCV generally involves only one election. On an RCV ballot, voters have the option to rank candidates in order of preference: first, second, third, and so forth. If no candidate receives a majority of the first-place votes, the candidate with the fewest first-place votes is eliminated and the votes are then counted again. If a voter's first choice is eliminated, that vote is given to the voter's second choice. This process continues until one candidate receives a majority of the first-place votes. That candidate is declared the winner. In 2022, midterm elections held in Seattle, Washington; Portland, Oregon; Fort Collins, Colorado; and other cities endorsed RCV. The state of Nevada recently endorsed RCV for some elections. According to the National Conference of State Legislatures, more than 50 RCV proposals have been introduced since 2018. Currently Alaska and Maine, and at least 62 other jurisdictions around the country have adopted RCV. Example 8 Electing the Veterans Club President Using the Plurality with Elimination Method Use the plurality with elimination method to determine the winner of the election for president of the Veterans Club from Example 2. The preference table is shown again in Table 14.8. Recall that A represents Antoine, B represents Betty, C represents Carlos, and D represents Don. Table 14.8 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
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