904 CHAPTER 14 Voting and Apportionment Solution First we count the number of first-place votes for each candidate: Antoine: 7 Betty: 19 Carlos: 17 Don: 11 Since 54 votes were cast, a candidate must have at least 28 first-place votes to receive a majority. In this election, no candidate received a majority. Antoine has the fewest number of first-place votes, so he is eliminated. From column one of Table 14.8, we see that 19 voters ranked their preference as B, A, C, D. With A eliminated, we assume that those same 19 voters would now rank their preference as B, C, D. From column two in Table 14.8, 15 voters ranked their preference as C, A, D, B. With A eliminated, we assume that those same 15 voters would now rank their preference as C, D, B. We eliminate A from the other columns of the table in a similar manner. The new preference table with A eliminated is given in Table 14.9. Now try Exercise 29 Table 14.9 Veterans Club Preference Table After Antoine Is Eliminated Number of Votes 19 15 11 7 2 First B C D D C Second C D C C D Third D B B B B The number of first-place votes is now Betty: 19 Carlos: 17 Don: 18 Still, no candidate received a majority. Carlos now has the fewest number of firstplace votes, so he is eliminated. With Carlos eliminated, the new preference table is given in Table 14.10. Table 14.10 Veterans Club Preference Table After Carlos Is Eliminated Number of Votes 19 15 11 7 2 First B D D D D Second D B B B B The number of first-place votes is now Betty: 19 Don: 35 Don has a majority of first-place votes and is declared the winner using the plurality with elimination method. 7 The Veterans Club elections in the previous examples are quite interesting. When the plurality method was used, Betty was declared the winner. When the Borda count method was used, Antoine was declared the winner. When the plurality with elimination method was used, Don was declared the winner. This dilemma, once again, underscores the importance of publicly stating the voting method to be used before the election takes place. The selection of the city to host the Olympic Games occurs by using a type of plurality with elimination. The election process for the Academy Awards involves
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