902 CHAPTER 14 Voting and Apportionment Even though Antoine received the fewest number of first-place votes, he is declared the winner under the Borda count method. Notice that with both the zoo logo election (Examples 3 and 5) and the Veterans Club president election (Examples 4 and 6), the plurality method and the Borda count method produced different winners. This result indicates the importance of choosing a voting method prior to the election. This will become even more evident when we examine the remaining voting methods. Next we will examine the plurality with elimination method, which also takes voters’ second and subsequent preferences into account. Plurality with Elimination The next method we will discuss, plurality with elimination, may involve a series of elections. When using the plurality with elimination method each voter votes for only one candidate. If a candidate initially receives a majority of votes, that candidate is declared the winner. If no candidate receives a majority of votes, the candidate with the fewest number of votes is eliminated and a second election is held. This process continues until a candidate receives a majority of votes. PLURALITY WITH ELIMINATION METHOD 1. Each voter votes for one candidate. 2. If a candidate receives a majority of votes, that candidate is declared the winner. 3. If no candidate receives a majority, eliminate the candidate with the fewest votes and hold another election. (If there is a tie for the fewest votes, eliminate all candidates tied for the fewest votes.) 4. Repeat this process until a candidate receives a majority. PROCEDURE One of the immediate disadvantages of the plurality with elimination method is the possible need for two or more elections, depending on the number of candidates. One way to limit the number of elections held is to begin with a runoff election in which voters choose among a field of candidates. In the second election, the voters only select among the top two candidates from the runoff election. Another way to avoid multiple elections entirely is to have voters rank candidates from most to least favorable just as we did with the Borda count method. We assume that in the first round, the voters would have selected their first choice. We must also assume that after a candidate is eliminated, the order of preference is not changed. For instance, let’s say that a voter’s original ranking order was E, G, B, D, F. Suppose that B is eliminated. This voter’s ranking order now becomes E, G, D, F. In this book, when working the examples and exercises, we will assume that the order preference remains the same in the second election as it was in the first election. The next two examples will demonstrate the plurality with elimination method. Example 7 Selecting a Zoo Logo Using the Plurality with Elimination Method Once again, we will consider the zoo logo election at the San Francisco Zoo. Recall that T represents tiger, K represents kangaroo, and G represents giraffe. Which animal is selected using the plurality with elimination method? Oleg Znamenskiy/Shutterstock
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