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# The possibilities of voting

(See attached files for full problem description)

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1. Four members are running for president of the Local Math Club - Alicia (a), Brice (b), Charlie (c), and Destiny (d). The voter profile is summarized in the table.
Use the Hare method to determine the winner.

Number of voters Ranking
17 c > d > a > b
11 a > c > d > b
8 d > c > a > b
4 b > a > c > d
1 a > d > c > b

2. The Science club is holding an election for president of the organization. Each member ranks the candidates from first to third. The voter profile given below shows the results of the ballot with candidates Carter (c), John (j), and Sean (s).
Use the pairwise comparison method to determine the winner.

Number of voters Ranking
7 j > s > c
11 s > j > c
3 j > c > s
8 c > s > j

3. A poll by fifteen sports announcers predicts the winner of the NCAA Basketball Final Four Teams: Louisiana State University (LSU) , University of California at Los Angeles (UCLA), George Mason (GM), and Florida (F). If the individual rankings are as summarized below, which team wins if they use a rank method that assigns 5, 3, 2 points and 1 point(s) to each first, second, third and fourth choice respectively?

Number of Announcers Ranking
5 UCLA>F> SU>GM
6 F>UCLA>LSU>GM
2 LSU>GM>F>UCLA
2 GM>LSU>F>UCLA

4. A seventeen-member committee must elect one of four candidates: R, S, T, or W. Their preference schedule as shown below. Which candidate wins under pairwise sequential voting with the predetermined order S, T, W, R?

Number of Members Ranking
6 R > S > T > W
5 S > R > T > W
3 T > S > R > W
3 W > T > S > R

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