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Math+103+Section+11+Sample+for+Exam+1 -...

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Math 103, Section 11       Exam #1-Sample    February 27, 2011  Name____________________ Please show your work. There are 11 problems. Formulas: 1+2+3+…+L=  L (L+1)                                            2 Formulas: 1+2+3+…+N-1=  (N-1)N                                                       2 Part I: Use the preference schedule below to answer the questions that follow. Number of  voters 27 19 9 15 2 1 st  choice B A D C A 2 nd  choice A D C A C 3 rd  choice D C A D D 4 th  choice C B B B B 1. 20 points   a.  How many people voted in this election? b. Rank the candidates using the extended Borda Count method. First place:      Second place:     Third place:         Fourth place: c.  Use the method of pairwise comparisons to determine the winner of the election. d.  Is there a Condorcet candidate?     If Yes, which candidate is a Condorcet candidate?  Explain your answer. e.  Use the extended plurality-with-elimination method to rank the candidates. First place:      Second place:     Third place:         Fourth place: f. Does the plurality-with-elimination method violate the Condorcet criterion?     
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Explain your answer. g.   After the election, it is decided for some reason that it is necessary to hold a revote.  What would have to happen to make us conclude that the plurality method violates the  independence of irrelevant alternatives (IIA) criterion? Be as specific as possible. That is, say  which candidate won, etc  Then what happened. h. State Arrow’s Impossibility Theorem
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