Exam 9: Social Choice: the Impossible Dream

If there are an odd number of voters, there is always a Condorcet winner.

Consider the following preference table: $\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\text { Number of oters }$ 3 2 2 First choice A B C Second choice B C B Third choice C A A Which candidate will be chosen if majority rule is used?

In order to choose which type of music to listen to in a student center music lounge, a Condorcet vote is held by the 15 students present. Below are the preference schedules for the students. Is there a Condorcet winner and, if so, which is it? $\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\text { Number of students }$ 6 5 4 First choice Classical Rock Rock Second choice Jazz Jazz Classical Third choice Rock Classical Jazz

Use the following information to answer the Questions Twenty-nine voters rank three candidates according to the following preference table. $\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\text { Number of voters }$ 3 9 8 9 First choice Second choice Third choice -Which candidate wins using plurality voting?

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 -Is there a Condorcet winner?

Use the following information to answer the Questions Your fly fishing club is attempting to decide where to go for the next day trip. The choices are Alder River (A), Boulder Pond (B), or Collie Creek (C). The preference rankings of the members are shown below. $\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\text { Number of members }$ 6 12 15 11 First choice Second choice Third choice -Which location, if any, is the Condorcet winner?

Use the following information to answer the Questions One hundred voters are to elect one of the four candidates: A, B, C, or D. Their preference schedule is shown below. $\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\text { Number of voters}$ 40 32 18 10 First choice A B D C Second choice C C C D Third choice B A B A Fourth choice D D A B -Which candidate wins using sequential pairwise voting with the agenda A, C, B, D?

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 B, D, A, C?

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 plurality voting?

Use the following information to answer the Questions Your fly fishing club is attempting to decide where to go for the next day trip. The choices are Alder River (A), Boulder Pond (B), or Collie Creek (C). The preference rankings of the members are shown below. $\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\text { Number of members }$ 6 12 15 11 First choice Second choice Third choice -Which location will be chosen if the Borda count is used?

Answer the following Questions using the preference table. $\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\text { Number of voters }$ 6 3 4 2 First choice A C C B Second choice B B D A Third choice C D A C Fourth choice D A B D -Which candidate will be chosen if sequential pairwise voting with agenda B, C, D, A is used?

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 -Which applicant will be given the position if the members use the Borda count to choose the new member?

Use the following information to answer the Questions Twenty-nine voters rank three candidates according to the following preference table. $\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\text { Number of voters }$ 3 9 8 9 First choice Second choice Third choice -Which candidate wins using Borda count?

The Borda count method of voting satisfies the independence of irrelevant alternatives criterion.

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 Borda count voting?

For a given set of voters' preference lists, different voting procedures may produce different winners.

Use the following information to answer the Questions Your fly fishing club is attempting to decide where to go for the next day trip. The choices are Alder River (A), Boulder Pond (B), or Collie Creek (C). The preference rankings of the members are shown below. $\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\text { Number of members }$ 6 12 15 11 First choice Second choice Third choice -Which location will be chosen if plurality voting is used?

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 X Chuck X X X X David X X X X Which pitcher is chosen if just one is to be selected?

In how many ways can you rank three candidates if ties are allowed?

Use the following information to answer the Questions Thirty board members must vote on five candidates: X, Y, Z, U, and V. Their preference rankings are summarized in the table below. $\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\text { Number of students }$ 12 10 8 First choice Second choice Third choice Fourth choice Fifth choice -Find the winner using sequential pairwise voting with the agenda X, Y, Z, U, V.