Exam 9: Social Choice: the Impossible Dream

Use the following information to answer Questions Fifty voters who elect one of the five candidates -A, B, C, D, or E-have the preference schedule shown below. $\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\text { Number of voters }$ 20 14 10 6 First choice Second choice Third choice Fourth choice Fifth choice -Which candidate will be elected using the Borda count?

Use the following preference table to answer the Questions $\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\text { Number of voters }$ 1 1 1 First choice A C B Second choice B A D Third choice D B C Fourth choice C D A -Which candidate wins using sequential pairwise voting with agenda C, A, B, D?

Use the following information to answer the Questions: There are 18 delegates to a political party's convention at which four people -A, B, C, and D- have been nominated as the party's candidate for governor. The delegates' preference schedule is shown below. $\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\text { Number of delegates }$ 8 9 4 First choice A B C Second choice B A B Third choice C D A Fourth choice D C D -What nominee would be elected if the party uses a rank system that assigns 5, 4, 1, and 0 point(s) for a first, second, third, and fourth choice, respectively? Is this result different from that which results from a Borda count?

Use the following information to answer Questions Consider a 13-person committee that is considering three applicants, A, B, and C, for an opening. The individual rankings are summarized in the table below. $\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\text { Number of members }$ 5 4 2 2 First choice Second choice Third choice -Which applicant would be accepted if the committee used the plurality-runoff method?

After their star pitcher moved to another town, the eight remaining members of the company baseball team needed to select a new pitcher. They used approval voting on the four prospects, and the results are listed below. An X indicates an approval vote. Alan X X X Bob X X X X Chuck X X X David X X X X X Which pitcher is chosen if just one is to be selected?

Explain May's Theorem.

Use the preference schedule of 23 voters for three candidates (A, B, and C) shown below to answer the following Questions $\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\text { Number of students }$ 8 5 6 4 First choice Second choice Third choice -Can the four voters in the last column vote strategically to change the outcome of Question 12 to one they would like better? Why or why not?

Use the following information to answer the Questions: Seventeen board members vote on four candidates, A, B, C, or D, for a new position on their board. Their preference schedules are shown below. $\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\text { Number of members }$ 7 6 4 First choice Second choice Third choice Fourth choice -Which candidate will be selected if they use the Hare system?

Consider a 13-person committee that is considering three applicants-A, B, and C-for an opening. The individual rankings are summarized in the table below. Which applicant would be accepted if the committee used the Borda count? $\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\text { Number of members }$ 5 4 2 2 First choice Second choice Third choice

Plurality voting fails to satisfy the Condorcet winner criterion (CWC).

Use the following preference table to answer the Questions: $\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\text { Number of voters }$ 3 3 2 3 First choice A C A D Second choice B D D C Third choice C B C B Fourth choice D A B A -Which candidate wins using Condorcet's system?

Explain why majority rule is not a good way to choose among four alternatives.

Sequential pairwise voting satisfies the Pareto condition.

Use the following information to answer the Questions: An 11-member committee must choose one of the four applicants -K, L, M, and N-for membership on the committee. The committee members have preferences among the applicants as given below. $\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\text { Number of members }$ 6 2 3 First choice Second choice Third choice Fourth choice -Who wins under the plurality method? Who wins under the plurality runoff method?

Use the following information to answer the Questions A group of 22 young people must decide whether to go to the beach (B), the mountain (M), or the zoo (Z) on a field trip. Their preference rankings are summarized in the table below. $\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\text { Number of voters}$ 10 8 4 First choice Second choice Third choice -Which choice wins using the Borda count?

Twenty-nine voters must choose from among three alternatives: A, B, and C. The voters' preference schedules are shown below. Which alternative wins using the Hare system? $\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\text { Number of voters}$ 12 8 6 3 First choice Second choice Third choice

Consider the following preference table: $\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\text { Number of voters }$ 3 2 2 First choice A B C Second choice B C B Third choice C A A Which candidate, if any, is the Condorcet winner?

Use the following information to answer the Questions Suppose that a nine-member committee needs to elect one of the four alternatives-A, B, C, or D. Their preference schedule is shown below. $\quad$$\quad$$\quad$$\quad$$\quad$$\text { Number of members }$ 4 3 2 First choice Second choice Third choice Fourth choice -What is the Borda score of the alternative A?

Use the following information to answer Questions Consider a 13-person committee that is considering three applicants, A, B, and C, for an opening. The individual rankings are summarized in the table below. $\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\text { Number of members }$ 5 4 2 2 First choice Second choice Third choice -Which applicant would be accepted if the committee used the plurality method?

Use the following information to answer the Questions: There are 18 delegates to a political party's convention at which four people -A, B, C, and D- have been nominated as the party's candidate for governor. The delegates' preference schedule is shown below. $\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\text { Number of delegates }$ 8 9 4 First choice A B C Second choice B A B Third choice C D A Fourth choice D C D -What nominee would be elected if the party uses a Borda count?