896 CHAPTER 14 Voting and Apportionment The planning committee for the San Francisco Zoo is voting on an animal for the new zoo logo. How should it determine the winner of this election? Is there more than one way to determine the winner? In this section, we will discuss four of the most popular voting methods. We will discover that the voting method chosen can greatly affect the results of an election. Voting Methods SECTION 14.1 LEARNING GOALS Upon completion of this section, you will be able to: 7 Use the plurality method to determine the winner of an election. 7 Use the Borda count method to determine the winner of an election. 7 Use the plurality with elimination method to determine the winner of an election. 7 Use the pairwise comparison method to determine the winner of an election. 7 Understand tie-breaking procedures for an election. Why This Is Important Voting methods are used in a variety of real-world problems from voting for our elected representatives to voting for a zoo logo to voting for the president of a student government. In a constitutional democracy, one of the most fundamental rights and responsibilities of its citizens is the right to vote. Voting gives voters a voice in decisions that affect our lives. Conducting a fair election to select representatives lies at the heart of a democratic form of government. In general, elections for public officials seem to be a simple proposition: You vote for the person you wish to represent you, and the candidate who obtains the most votes is elected. However, when more than one choice is involved in the election or when voters are asked to rank their choices, the selection is not as simple. The outcome of the election is greatly influenced by the voting method used, as will be discussed in this section. Consider the following example. The Ridgemoor Homeowners Association board of directors needs to choose one type of flower to plant at the main entrance to the housing development. The choices available are begonia, impatiens, marigold, or periwinkle. Each of the five directors is asked to rank the flowers according to preference. The results of this election are given in Table 14.1. Table 14.1 Ridgemoor Board of Directors Flower Choices Choice Charlie Denise Edwardo Gerry Joe First Impatiens Impatiens Impatiens Marigold Marigold Second Marigold Marigold Marigold Begonia Begonia Third Periwinkle Periwinkle Periwinkle Periwinkle Periwinkle Fourth Begonia Begonia Begonia Impatiens Impatiens If we were to run a simple election in which we only considered each director’s first choice, impatiens would be chosen. It also can be said that impatiens received a majority of first-place votes. A majority simply refers to receiving more than 50% of the votes. However, looking at the table, it appears that marigolds might be a better choice since all the directors have marigolds listed either as their first or second choice and impatiens are listed last by two directors. Definition: Majority A majority refers to receiving more than 50% of the votes in an election. Zhao jian kang/Shutterstock Gareth Boden/Pearson Education Ltd
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