Members of the board of directors of an association are voting to select a city to host their annual meeting. The board is considering the following cities: city L, city N, and city B. The preference table for the 31 members of the board of directors is shown to the right. Show that the Borda count method violates the majority Number of votes 16 11 4 First LNN Second criterion. Third В В ... Which of the following reasons explains why the Borda count violates the majority criterion? Choose the correct answer below. A. City N wins with the Borda count method but city L has a majority of first-place votes. B. City N wins with the Borda count method but city B has a majority of first-place votes. C. City L wins with the Borda count method and has a majority of first-place votes. D. City B wins with the Borda count method but city L has a majority of first-place votes.

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1/outline/file/44889344 1 O 6. a. Explain what the majority criterion states. b. In problem #2, which candidate did you determine to be the winner using the Borda count method? Has the majority criterion been violated? Why or why not? Explain clearly by stating in complete sentences. c. In a school election, there were 3 candidates: Aiden, Kyle and Brandon. The preference table is given below. Number of voters 18 17 21 28 K A K A A В' B K B K A B 1st Choice 2ND Choice 3rd Choice The winner of this election using the Borda count is Aiden (work is not shown for this). Has the majority criterion been violated? Why or why not? Explain clearly by stating your answer in complete sentences. 7. a. Explain what the monotonicity criterion states. b. Consider an election between Xu, Smith and Unger. The preference table is given below. The winner using the plurality-with-elimination method is Smith. Show work to verify this 100 Number of voters 1st Choice 2ND Choice 3rd Choice suspicion of voting…

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The city of Cleansburg has 8126 registered voters. There is an election for Mayor of Cleansburg, and there are three candidates for the position: Smith, Jones, and Brown. The day before the election a telephone poll of 517 randomly chosen registered voters produced the following results: 229 people surveyed indicated that they would vote for Smith, 175 indicated that they would vote for Jones, and 113 indicated that they would vote for Brown. a) Give the sampling proportion for this survey. Round the answer to two decimal places. % b) Give the sample statistic estimating the percentage of the vote going to Smith. Round the answer to two decimal places. %

2. Suppose that an employer decides to hire a new CEO using the Borda count. A panel of 35 managers, board members, and other executives rank the candidates using a preference ballot. Here is the preference schedule. 1st Place Chen Ashford Ashford 2nd Place Ashford Borge Chen 3rd Place Borge Chen Borge Voters 18 16 1 (a) Find the Borda count for each of the candidates to determine who will be hired. (b) Now forget the Borda counts and look at the number of first place votes. (c) Does any candidate have a majority of the votes? Which one? (d) Does Criterion 1 apply? Has Criterion 1 been satisfied? (e) Again, forget the Borda counts and look at the number of first place votes in pairwise comparisons. Who wins in a race between Chen and Ashford? between Chen and Borge? (f) Is there a Condorcet winner? Did the Condorcet winner win the election? (g) Does Criterion 2 apply? Has Criterion 2 been satisfied?