UTPA STEM/CBI Courses/Contemporary Mathematics/Voting and Social Choice/Test Your Mettle Quiz

Test Your Mettle Quiz

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1. The Arrowville Math Society is voting to select its next president from among Allen, Betty, and Christy. The society members vote using preference ballots, ranking the candidates from first choice to third choice. A summary of the ballots cast is shown in the following preference schedule.

   Number of Voters	10	14	6
   1st Choice	Allen	Betty	Cristy
   2nd Choice	Cristy	Allen	Allen
   3rd Choice	Betty	Cristy	Betty

   (a) Who will win the election if the society uses the plurality method?

   (b) Who will win the election if the society uses the plurality-with-elimination method?

   (c) Who will win the election if the society uses the Borda count method?

   (d) Who will win the election if the society uses the method of pairwise comparisons?

2. Identify the voting method used in each of the following elections.

   (a) Which voting method is used in the selection of Major League Baseball's Cy Young Award?

   (b) Which voting method is used to elect the mayor of San Francisco, California?

   (c) Which voting method is used by the Academy of Motion Picture Arts and Sciences for determining the Academy Award for Best Picture?

3. In the preference schedule below, candidate B would win using the Borda count method. If, however, candidate C drops out of the race and the Borda count method is used to find the winner of the election with C removed, candidate B would lose. This shows that the Borda count method violates which fairness criterion?

   Number of Voters	7	4	2
   1st Choice	A	B	D
   2nd Choice	B	D	A
   3rd Choice	C	C	C
   4th choice	D	A	B

4. (Multiple Choice) The UTRGV baseball team decides to use a new voting method for electing its team captain. Arrow's Impossibility Theorem implies which one of the following statements about this new voting method?

   A. It is impossible to have a vote end in a tie

   B. The voting method will be considered unfair by some voters.

   C. The voting method will fail at least one fairness criterion

   D. The voting method will fail every fairness criterion