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 Condorcet winner?

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 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 is chosen for the promotion if just one of them is to be selected?

A) A B) B C) F D) J A) A B) B C) F D) J

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 Hare system.

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

Exam 9: Social Choice: the Impossible Dream

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 -Is there a Condorcet winner?

(Multiple Choice)

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Question 101

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. $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\text { Voters }$ Candidates 1 2 3 4 5 -Which faculty member is chosen for the promotion if just one of them is to be selected?

(Multiple Choice)

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Question 102

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 the Hare system.

(Multiple Choice)

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(92)

Question 103

Urban Services

Business Efficiency

Planning and Scheduling

Linear Programming

Exploring Data: Distributions

Exploring Data: Relationships

Data for Decisions

Probability: the Mathematics of Chance

The Manipulability of Voting Systems

Weighted Voting Systems

Electing the President

Fair Division

Apportionment

Game Theory: the Mathematics of Competition

Identification Numbers

Information Science

Growth and Form

Symmetry and Patterns

Tilings

Savings Models

Borrowing Models

The Economics of Resources

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