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 }$ $\begin{array} { l c c c } & 12 & 10 & 8 \\ \text { First choice } & \mathrm { X } & \mathrm { Y } & \mathrm { Z } \\ \text { Second choice } & \mathrm { U } & \mathrm { Z } & \mathrm { U } \\ \text { Third choice } & \mathrm { Y } & \mathrm { X } & \mathrm { X } \\ \text { Fourth choice } & \mathrm { Z } & \mathrm { U } & \mathrm { V } \\ \text { Fifth choice } & \mathrm { V } & \mathrm { V } & \mathrm { Y } \end{array}$ -Find the winner using the Borda count.

A) X B) Y C) Z D) No winner is chosen. A) X B) Y C) Z D) No winner is chosen. A

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 }$ $\begin{array} { l c c c c } & 6 & 12 & 15 & 11 \\ \text { First choice } & \mathrm { A } & \mathrm { C } & \mathrm { B } & \mathrm { A } \\ \text { Second choice } & \mathrm { B } & \mathrm { B } & \mathrm { A } & \mathrm { C } \\ \text { Third choice } & \mathrm { C } & \mathrm { A } & \mathrm { C } & \mathrm { B } \end{array}$ -Which location will be chosen if sequential pairwise voting with agenda B, A, C is used?

A) Alder River B) Boulder Pond C) Collie Creek D) No winner can be chosen. A) Alder River B) Boulder Pond C) Collie Creek D) No winner can be chosen. C

Consider the following preference table: $ \quad$$ \quad$$ \quad$$ \quad$$ \quad$$ \quad$$ \quad$$ \quad$$\text { Number of voters }$ $\begin{array} { l l c c c } & 4 & 6 & 8 & 4 \\ \text { First choice } & \text { D } & \text { C } & \text { A } & \text { B } \\ \text { Second choice } & \text { C } & \text { B } & \text { D } & \text { A } \\ \text { Third choice } & \text { B } & \text { D } & \text { C } & \text { C } \\ \text { Fourth choice } & \text { A } & \text { A } & \text { B } & \text { D } \end{array}$ Which candidate will be chosen if the Borda count is used?

The answer of Consider the following preference table: $ \quad$\(...

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}$ $\begin{array} { l c c c c } & 40 & 32 & 18 & 10 \\ \text { First choice } & \text { A } & \text { B } & \text { D } & \text { C } \\ \text { Second choice } & \text { C } & \text { C } & \text { C } & \text { D } \\ \text { Third choice } & \text { B } & \text { A } & \text { B } & \text { A } \\ \text { Fourth choice } & \text { D } & \text { D } & \text { A } & \text { B } \end{array}$ -Which candidate wins using the Hare system?

A) A wins. B) B wins. C) D wins. D) No winner is determined. A) A wins. B) B wins. C) D wins. D) No winner is determined.

Use the following information to answer the Questions A five-member evaluating committee votes by approval voting on 10 faculty members for a promotion as indicated in the table below. An X indicates an approval vote. $ \quad$$ \quad$$ \quad$$ \quad$$ \quad$$ \quad$$ \quad$$ \quad$$\text { Voters }$ $\begin{array} { c c c c c c } \text { Candidates } &1 & 2 & 3 & 4 & 5 \\ \mathrm {~A} & \mathrm { X } & & \mathrm { X } & \mathrm { X } & \mathrm { X } \\ \mathrm { B } & \mathrm { X } & \mathrm { X } & \mathrm { X } & \mathrm { X } & \mathrm { X } \\ \mathrm { C } & & & \mathrm { X } & & \mathrm { X } \\ \mathrm { D } & & \mathrm { X } & \mathrm { X } & \mathrm { X } & \\ \mathrm { E } & \mathrm { X } & & \mathrm { X } & & \mathrm { X } \\ \mathrm { F } & \mathrm { X } & & & & \mathrm { X } \\ \mathrm { G } & & \mathrm { X } & \mathrm { X } & \mathrm { X } & \\ \mathrm { H } & & \mathrm { X } & & \mathrm { X } & \\ \mathrm { I } & \mathrm { X } & & \mathrm { X } & \mathrm { X } & \\ \mathrm { J } & & \mathrm { X } & \mathrm { X } & \mathrm { X } & \mathrm { X } \end{array}$ -Which faculty member(s) is(are) chosen if 60% approval is necessary and at most three are to be selected?

A) B only B) A, B, and J C) All candidates, except C, F, and H D) None will be promoted. A) B only B) A, B, and J C) All candidates, except C, F, and H D) None will be promoted.

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}$ $\begin{array} { l c c c c } & 40 & 32 & 18 & 10 \\ \text { First choice } & \text { A } & \text { B } & \text { D } & \text { C } \\ \text { Second choice } & \text { C } & \text { C } & \text { C } & \text { D } \\ \text { Third choice } & \text { B } & \text { A } & \text { B } & \text { A } \\ \text { Fourth choice } & \text { D } & \text { D } & \text { A } & \text { B } \end{array}$ -Is there a winner using the plurality-runoff method?

A) Yes, A wins. B) Yes, B wins. C) Yes, C wins. D) No winner is determined. A) Yes, A wins. B) Yes, B wins. C) Yes, C wins. D) No winner is determined.

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 }$ $\begin{array} { l c c c } & 4 & 3 & 2 \\ \text { First choice } & \mathrm { A } & \mathrm { B } & \mathrm { C } \\ \text { Second choice } & \mathrm { B } & \mathrm { D } & \mathrm { D } \\ \text { Third choice } & \mathrm { C } & \mathrm { A } & \mathrm { A } \\ \text { Fourth choice } & \mathrm { D } & \mathrm { C } & \mathrm { B } \end{array}$ -Which alternative wins using sequential pairwise voting with the agenda A, B, C, D?

A) A B) B C) C D) D A) A B) B C) C D) D

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 Borda count? $ \quad$$ \quad$$ \quad$$ \quad$$ \quad$$ \quad$$ \quad$$ \quad$$\text { Number of students }$ $\begin{array} { l l l l l l } & 3 & 3 & 2 & 2 & 2 \\ \text { First choice } & \mathrm { B } & \mathrm { M } & \mathrm { S } & \mathrm { B } & \mathrm { S } \\ \text { Second choice } & \mathrm { M } & \mathrm { B } & \mathrm { M } & \mathrm { S } & \mathrm { B } \\ \text { Third choice } & \mathrm { S } & \mathrm { S } & \mathrm { B } & \mathrm { M } & \mathrm { M } \end{array}$

A) S B) M C) B D) No winner can be chosen. A) S B) M C) B D) No winner can be chosen.

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. Is there a Condorcet winner among the pizza types? $ \quad$$ \quad$$ \quad$$ \quad$$ \quad$$ \quad$$ \quad$$ \quad$$\text { Number of students }$ $\begin{array} { l l l l l l } & 3 & 3 & 2 & 2 & 2 \\ \text { First choice } & \mathrm { B } & \mathrm { M } & \mathrm { S } & \mathrm { B } & \mathrm { S } \\ \text { Second choice } & \mathrm { M } & \mathrm { B } & \mathrm { M } & \mathrm { S } & \mathrm { B } \\ \text { Third choice } & \mathrm { S } & \mathrm { S } & \mathrm { B } & \mathrm { M } & \mathrm { M } \end{array}$

A) S B) M C) B D) No winner can be chosen. A) S B) M C) B D) No winner can be chosen.

Use the following information to answer the Questions A five-member evaluating committee votes by approval voting on 10 faculty members for a promotion as indicated in the table below. An X indicates an approval vote. $ \quad$$ \quad$$ \quad$$ \quad$$ \quad$$ \quad$$ \quad$$ \quad$$\text { Voters }$ $\begin{array} { c c c c c c } \text { Candidates } &1 & 2 & 3 & 4 & 5 \\ \mathrm {~A} & \mathrm { X } & & \mathrm { X } & \mathrm { X } & \mathrm { X } \\ \mathrm { B } & \mathrm { X } & \mathrm { X } & \mathrm { X } & \mathrm { X } & \mathrm { X } \\ \mathrm { C } & & & \mathrm { X } & & \mathrm { X } \\ \mathrm { D } & & \mathrm { X } & \mathrm { X } & \mathrm { X } & \\ \mathrm { E } & \mathrm { X } & & \mathrm { X } & & \mathrm { X } \\ \mathrm { F } & \mathrm { X } & & & & \mathrm { X } \\ \mathrm { G } & & \mathrm { X } & \mathrm { X } & \mathrm { X } & \\ \mathrm { H } & & \mathrm { X } & & \mathrm { X } & \\ \mathrm { I } & \mathrm { X } & & \mathrm { X } & \mathrm { X } & \\ \mathrm { J } & & \mathrm { X } & \mathrm { X } & \mathrm { X } & \mathrm { X } \end{array}$ -Which candidate(s) receive(s) a promotion if 80% approval is needed?

A) B only B) A, B, and J C) All candidates, except C, F, and H D) No candidate receives a promotion. A) B only B) A, B, and J C) All candidates, except C, F, and H D) No candidate receives a promotion.