14.1 Voting Methods 907 As we have illustrated, using four different voting methods resulted in four different winners for the president of the Veterans Club. Using the plurality method, Betty was the winner. Using the Borda count method, Antoine was the winner. Using the plurality with elimination method, Don was the winner. Using the pairwise comparison method, Carlos was the winner. Each candidate could claim that they should be declared the winner. Thus, the voting method we choose to use could greatly affect the election results and therefore should be chosen prior to an election. Since we have 4 candidates, n 4, = the number of comparisons needed is c n n( 1) 2 4(3) 2 6 = − = = The 6 comparisons we will make are A versus B, A versus C, A versus D, B versus C, B versus D, and C versus D. 1. The pairwise comparison of Antoine versus Betty is + + + = Antoine: 15 11 7 2 35 votes Betty: 19 votes Antoine wins this comparison and is awarded 1 point. 2. The pairwise comparison of Antoine versus Carlos is + = + + = Antoine: 19 7 26 votes Carlos: 15 11 2 28 votes Carlos wins this comparison and is awarded 1 point. 3. The pairwise comparison of Antoine versus Don is + + = + = Antoine: 19 15 7 41 votes Don: 11 2 13 votes Antoine wins this comparison and is awarded a second point. 4. The pairwise comparison of Betty versus Carlos is + + + = Betty: 19 votes Carlos: 15 11 7 2 35 votes Carlos wins this comparison and is awarded a second point. 5. The pairwise comparison of Betty versus Don is + + + = Betty: 19 votes Don: 15 11 7 2 35 votes Don wins this comparison and is awarded 1 point. 6. The pairwise comparison of Carlos versus Don is + + = + = Carlos: 19 15 2 36 votes Don: 11 7 18 votes Carlos wins this comparison and is awarded a third point. We have made all possible one-to-one comparisons. Antoine received 2 points, Betty received 0 points, Carlos received 3 points, and Don received 1 point. Since Carlos received 3 points, the most points from the pairwise comparison method, Carlos wins the election. 7 Now try Exercise 33 Did You Know? Presidential Elections m Rutherford B. Hayes lost the popular vote, but won the electoral college and the election. Since the United States was founded in 1776, Americans and their elected representatives have had many disputes regarding election procedures. As you read through this chapter, you will see various voting methods that were used to try to make the voting procedures as fair as possible. You will also learn that there is no ideal voting method, that is, one that has no flaws. Although there may be flaws in the voting procedures, the American election procedure is still a model to democracies all around the world. One current debate is whether we should continue using our present electoral system or change to use the popular vote to decide presidential elections. As of this writing, five presidents were elected even though they lost the popular vote: John Quincy Adams (1824), Rutherford B. Hayes (1876), Benjamin Harrison (1888), George W. Bush (2000), and Donald Trump (2016). Tie Breaking Just as the four methods we have examined can produce four different winners, each method could also produce a tie between two or more candidates. In each of the previous examples, the voting method used led to one winner, but that is not always the case. With each method described—plurality method, Borda count method, plurality with elimination method, and pairwise comparison method—the possibility of the method producing a tie is very real. A tie could be achieved simply by having only two candidates each with the same number of supporters. Breaking a tie can be achieved either by making an arbitrary choice, such as flipping a coin, or by bringing in an additional voter. For example, under Robert’s Rules James Landy/Library of Congress Prints and Photographs Division [LC-USZ62-64279]
RkJQdWJsaXNoZXIy NjM5ODQ=