Exam 9: Social Choice: the Impossible Dream

If the winner of an election is not affected by moving that winner higher on some voting ballets with no other changes, the voting system is satisfying:

A group of 12 students have to decide among three types of pizza: sausage (S), mushroom (M), and beef (B). Their preference rankings are shown below. Which choice will the group make if they use the Hare system? $\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\text { Number of students }$ 3 3 2 2 2 First choice Second choice Third choice

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 Hare system?

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 Hare system is used?

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 -If a rank method is used, which candidate, if any, wins in a straight plurality election?

Explain how the plurality runoff voting system might not choose a winner.

A group of 12 students have to decide among three types of pizza: sausage (S), mushroom (M), and beef (B). Their preference rankings are shown below. Which choice will the group make if they use the plurality-runoff voting method? $\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\text { Number of students }$ 3 3 2 2 2 First choice Second choice Third choice

Use the following information to answer the Questions Eight board members vote by approval voting on four candidates-A, B, C, and D-for new positions on their board as indicated in the following table. An X indicates an approval vote. $\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\text { Voters }$ 1 2 3 4 5 6 7 8 -Which candidate will be chosen for the board if just one of them is to be elected?

Use the following information to answer the Questions Eight board members vote by approval voting on four candidates-A, B, C, and D-for new positions on their board as indicated in the following table. An X indicates an approval vote. $\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\text { Voters }$ 1 2 3 4 5 6 7 8 -Which candidate(s) is(are) elected if 80% approval is necessary and at most two are elected?

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 runoff?

Explain when a voting system is subject to manipulability.

A group of 12 students have to decide among three types of pizza: sausage (S), sushroom (M), and seef (B). Their preference rankings are shown below. Which choice will the group make if they use sequential pairwise voting with agenda B, M, S? $\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\text { Number of students }$ 3 3 2 2 2 First choice Second choice Third choice

How many votes are needed for a majority winner if there are 25 voters?

A 17-member committee must elect one of four candidates: R, S, T, or W. Their preference schedule is shown below. Which candidate wins under pairwise sequential voting with the agenda S, T, W, R? $\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\text { Number of members }$ 6 4 3 First choice Second choice Third choice Fourth choice

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 -Which candidate wins if an election is held between A and C and the winner of that race runs against B?

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 Hare system?

Explain why approval voting is not a perfect voting system.

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 -Who wins using the plurality method? Do the results change if the plurality runoff method is used?

A group of 12 students have to decide among three types of pizza: sausage (S), mushroom (M), and beef (B). Their preference rankings are shown below. Which choice will the group make if they use plurality voting? $\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\text { Number of students }$ 3 3 2 2 2 First choice Second choice Third choice

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 -If a Borda count is used that assigns 3 points for a first-place vote, 2 points for a second-place vote, and 1 point for a third-place vote, who wins the election?