Math 103 Final Exam Review Problems

Math 103 Final Exam Review Problems - Practice Problems for...

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Practice Problems for Math 103 Final (Fall 2011) 1. Suppose there are 5 candidates, Allison, Bill, Clint, Diana, and Evan ( A , B , C , D ¸ and E respectively) running for student office in a local high school. Each of the 470 gives their preference. The winner of the election is given the title of president; the runner-up is given the title of vice president followed by secretary, treasurer, and PR. The results of the election are below: Number of Voters 150 120 100 60 40 1 st Choice E C B D B 2 nd Choice C B D C D 3 rd Choice B D A B E 4 th Choice A E C A A 5 th Choice D A E E C a. Rank the candidates of this election using the Borda Count Method . (5 points) b. Rank the candidates of this election using the Plurality with Elimination Method . (5 points) c. Is there a Condorcet candidate? If so, who is it? Explain your answer. (3 points) d. If the Borda Count Method is used to determine the winner of this election, has a violation of the Condorcet Criterion occurred? Explain your answer. (3 points) e. If the Plurality with Elimination Method is used to determine the winner of this election, has a violation of the Condorcet Criterion occurred? Explain your answer. (3 points) 2. A student claims that any candidate who wins an election using the Plurality Method must be a Majority candidate . Give a simple example to show that the student is incorrect. (5 points) 3. Consider an election with 12 candidates. Suppose the Method of Pairwise Comparisons is used to determine the winner. a. How many pairwise comparisons are there? (3 points) b. If it takes approximately 45 seconds to calculate the winner in a pairwise comparison, how long will it take to determine the winner of the election? (5 points)
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4. True or False: For each of the following, state whether the claim is True or False. (2 points each) a. In an election between Bryan, Clement, Maika, and Rebecca, Bryan wins the election. For some reason, it turns out that Rebecca was not eligible to run and she is disqualified. A re-election is held and Maika wins. This is a violation of the IIA Criterion . b. Suppose in an election between Alyssa, Christina, Joshua, and Sabine, the winner is Joshua. Suppose for some reason, a re-election occurs and the only difference is that some voters changed their votes from the column on the left to the column on the right. 1 st Alyssa 2 nd Joshua 3 rd Christina 4 th Sabine Joshua Christina Sabine Alyssa c. Christina is the winner of the new election. This is a violation of the Monotonicity Criterion . d. If the Method of Pairwise Comparison s is used to determine the winner of an election, then that candidate is a Condorcet candidate . e. In any weighted voting system, there cannot be more than one player with veto power. f.
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Math 103 Final Exam Review Problems - Practice Problems for...

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