Question 1

What does Dana have at the end of the process?

Accepted Answer

A)  $\$ 2$ 
B)  $\$ 3 \frac { 1 } { 2 }$ 
C)  $\$ 3 \frac { 3 } { 16 }$ 
D)  $\$ 2 \frac { 15 } { 16 }$ 
A)  $\$ 2$ 
B)  $\$ 3 \frac { 1 } { 2 }$ 
C)  $\$ 3 \frac { 3 } { 16 }$ 
D)  $\$ 2 \frac { 15 } { 16 }$ D

Question 2

Use the following information to answer the Questions
At the end of the lease on their apartment, Toni and Terry decide to rent separate places and so must make a fair division of the property they purchased together. The items to be divided and the point values each person places on them are given below. $$\begin{array} { l l l } 
\text { Item } & \text { Toni's points } & \text { Terry's points } \
\text { CD player } & 15 & 20 \
\text { Sofa } & 30 & 25 \
\text { Microwave } & 20 & 25 \
\text { TV } & 35 & 30
\end{array}$$
-If Toni and Terry use the adjusted winner procedure to divide the property, what will Terry end with?

Accepted Answer

A)  CD player, microwave, and TV 
B)  CD player, microwave, and 1/6 TV 
C)  CD player and microwave only 
D)  CD player, microwave, and 4/13 TV 
A)  CD player, microwave, and TV 
B)  CD player, microwave, and 1/6 TV 
C)  CD player and microwave only 
D)  CD player, microwave, and 4/13 TV D

Question 3

Use the following information to answer the Questions 
Albert, Bella, Cosmo, and Dante inherit their grandmother's estate, which consists of a rare first- edition novel and a piano. The dollar values that each heir places on the items are as follows: $\begin{array}{l}
\begin{array}{lll}
\underline{\text { Object }} & \underline{\text { Albert }} & \underline{\text { Bella }}\
\text { Novel }&10,000&6,000\
\text { Piano } & 2,000 & 5,000
\end{array}
\begin{array}{lll}
\underline{\text { Cosmo }}&\underline{\text { Dante }} \
500&100\
4,000 & 100
\end{array}
\end{array}$
 Use the Knaster inheritance procedure to divide the property.
-How much cash does Dante end up with?

Accepted Answer

$2068.75

Question 4

The administration and the student body at a local college are at odds over several issues. The relative importance of each issue to each group is as follows: $\begin{array}{lcc}
\underline{\text { Issue }} & \underline{\text { Administration's }} & \underline{\text { 
Student's points }} \
&\underline{\text { points }}\
\text { Mandatory meal plan } & 40 & 15 \
\text { Mandatory campus living } & 5 & 30 \
\text { Cars on campus } & 5 & 20 \
\text { Campus curfew } & 10 & 15 \
\text { Weekday fraternity parties } & 40 & 20
\end{array}$ Use the adjusted winner procedure to determine a fair resolution.

Accepted Answer

The administration gets its wa

Question 5

Four heirs need to make a fair division of the property left in an estate. The objects and the point values assigned to them are given below. The heirs want to use the trimming procedure, with the order Chris, Kelly, Dana, and Kim. Chris divides the estate into the following parts: (1) house, (2) car and 10 points from money, (3) painting and 10 points from money, (4) furniture and 15 points from money, and (5) remaining 20 points from money. Which parts will Kelly trim? $\begin{array} { lccc} 
\text { Object } & \text { Chris's points } & \text { Kelly's points } & \text { Dana's points } & \text { Kim's points } \
\text { House } & 20 & 15 & 18 & 25 \
\text { Car } & 10 & 12 & 10 & 5 \
\text { Painting } & 10 & 8 & 12 & 15 \
\text { Fumiture } & 5 & 10 & 10 & 5 \
\text { Money } & 55 & 55 & 50 & 50
\end{array}$

Accepted Answer

A)  part #4 only 
B)  parts #2, #3, and #4 
C)  parts #2 and #4 
D)  none 
A)  part #4 only 
B)  parts #2, #3, and #4 
C)  parts #2 and #4 
D)  none

Question 6

Use the following information to answer the Questions:
Alex, Betty, and Chris each view a cake as shown below. They will share the cake using the last-diminisher method with the order Alex, Betty, and Chris cutting and passing off the right side of the cake.  
-Though they don't realize it, Dana, Chris, Kelly, and Terry each view a cake the same way. They will share the cake using the last-diminisher method, in the order given above. When the first person cuts and passes a piece of the cake, who eventually retains this piece?

Accepted Answer

A)  Dana 
B)  Chris 
C)  Kelly 
D)  Terry 
A)  Dana 
B)  Chris 
C)  Kelly 
D)  Terry

Question 7

Suppose Dave and Merrie want to take turns, using the bottom-up strategy, to allocate six treats. Their ranked preferences are listed below: $\begin{array}{|ll|l|l|l|l|l|}
\hline \text { Dave } & \begin{array}{l}
\text { lst } \
\text { gummy } \
\text { worms }
\end{array} & \begin{array}{l}
2^{\text {nd }} \
\text { chocolate } \
\text { bar }
\end{array} & \begin{array}{l}
3 r \mathrm{rd} \
\text { lemon } \
\text { cookies }
\end{array} & \begin{array}{l}
\text { th } \
\text { chips }
\end{array} & \begin{array}{l}
\text { 5th } \
\text { cheese- } \
\text { cake }
\end{array} & \begin{array}{l}
6^{\text {th }} \
\text { pretzels }
\end{array} \
\hline \text { Merrie } & \begin{array}{l}
\text { lemon } \
\text { cookies }
\end{array} & \begin{array}{l}
\text { chocolate } \
\text { bar }
\end{array} & \text { chips } & \begin{array}{l}
\text { gummy } \
\text { worms }
\end{array} & \text { pretzels } & \begin{array}{l}
\text { cheese- } \
\text { cake }
\end{array} \
\hline
\end{array}$If Dave chooses first, what is the division of the objects?

Accepted Answer

Dave gets chocolate

Question 8

Use the following information to answer the Questions:
Suppose Kim and Chris want to take turns, using the bottom-up strategy, to allocate several textbooks currently held jointly. Their ranked preferences are listed below: $$\begin{array} { | l | l | l | l | l | l | l | } 
\hline & 1 ^ { \text {st } } & 2 ^ { \text {nd } } & 3 ^ { \text {nd } } & 4 ^ { \text {th } } & 5 ^ { \text {th } } & 6 ^ { \text {th } } \
\hline \text { Chris } & \text { botany } & \text { sociology } & \text { physiology } & \text { biology } & \text { ecology } & \text { chemistry } \
\hline \text { Kim } & \text { biology } & \text { chemistry } & \text { botany } & \text { sociology } & \text { ecology } & \text { physiology } \
\hline
\end{array}$$
-If Chris chooses first, when is the sociology book chosen?

Accepted Answer

A)  It is Chris's first choice. 
B)  It is Chris's second choice. 
C)  It is Kim's second choice. 
D)  It is Kim's third choice. 
A)  It is Chris's first choice. 
B)  It is Chris's second choice. 
C)  It is Kim's second choice. 
D)  It is Kim's third choice.

Question 9

Use the following information to answer the Questions:
Suppose Jack and Joe want to take turns, using the bottom-up strategy, to allocate a selection of cookies. Their ranked preferences are listed below: $$\begin{array} { l l l l l l l } 
& \text { 1st } & \text { 2nd } & 3 \text { rd } & \text { 4th } & 5 \text { th } & 6 \text { th } \
\text { Jack } & \text { chocolate } & \text { peanut butter } & \text { macadamia } & \text { macaroon } & \text { sugar } & \text { oatmea } \
\text { Joe } & \text { peanut butter } & \text { oatmeal } & \text { macaroon } & \text { macadamia } & \text { chocolate } & \text { sugar }
\end{array}$$
-If Jack chooses first, when is the chocolate cookie chosen?

Accepted Answer

A)  It is Jack's second choice. 
B)  It is Joe's second choice. 
C)  It is Jack's third choice. 
D)  It is Joe's third choice. 
A)  It is Jack's second choice. 
B)  It is Joe's second choice. 
C)  It is Jack's third choice. 
D)  It is Joe's third choice.

Question 10

Andi, Chris, and Kim must make a fair division of a car left to them by their father. Using the Knaster inheritance procedure, the values they bid on the car are given below. Find the results of the fair division.
$\begin{array}{lccc}
 &\text { Andi}& \text { Chris}& \text { Kim }\
 \text { Car } &\$ 2400& \$ 3000& \$ 2700
\end{array}$

Accepted Answer

A)  Chris gets the car and pays $1900; Andi gets $900, and Kim gets $1000. 
B)  Chris gets the car, Andi gets $800; Kim gets $900. 
C)  Chris gets the car and pays $1500; Andi gets $1200, and Kim gets $1350. 
D)  Chris gets the car and pays $2550; Andi gets $1200, and Kim gets $1350. 
A)  Chris gets the car and pays $1900; Andi gets $900, and Kim gets $1000. 
B)  Chris gets the car, Andi gets $800; Kim gets $900. 
C)  Chris gets the car and pays $1500; Andi gets $1200, and Kim gets $1350. 
D)  Chris gets the car and pays $2550; Andi gets $1200, and Kim gets $1350.

Question 11

What is the net value to Brook of her inheritance?

Accepted Answer

A)  $\$ 4$ 
B)  $\$ 3 \frac { 7 } { 16 }$ 
C)  $\$ 6$ 
D)  $10 
A)  $\$ 4$ 
B)  $\$ 3 \frac { 7 } { 16 }$ 
C)  $\$ 6$ 
D)  $10

Question 12

A husband and wife are getting divorced. The property to be divided, and the relative value of the items to each, are as follows: $$\begin{array} { l c c } 
\text { Object } & \begin{array} { c } 
\text { Husband's } \
\text { points }
\end{array} & \text { Wife's point } \
\text { House } & 30 & 15 \
\text { Car } & 25 & 25 \
\text { Cabin } & 20 & 40 \
\text { Boat } & 16 & 15 \
\text { Television } & 5 & 3 \
\text { Stereo } & 4 & 2
\end{array}$$ Use the adjusted winner procedure to determine a fair division of the property.

Accepted Answer

The husband gets the house, th

Question 13

Does Ashley get more than one quarter of what she thinks the inheritance is worth?

Accepted Answer

A) True 
 B)False

Question 14

What is the name of the fair-division procedure where one party divides the object into two parts in any way that he desires, and the other party chooses whichever part she wants?

Accepted Answer

A)  division using bottom-up strategy 
B)  divide-and-choose 
C)  taking turns 
D)  envy-free division 
A)  division using bottom-up strategy 
B)  divide-and-choose 
C)  taking turns 
D)  envy-free division

Question 15

Use the following information to answer the Questions
Tom and Sandy must make a fair division of three objects left by their great-aunt Sally. They have assigned points to the objects as shown below. $$\begin{array} { l c c } 
\text { Object } & \text { Tom's points } & \text { Sandy's points } \
\text { Painting } & 40 & 30 \
\text { Jewelry } & 10 & 50 \
\text { Car } & 50 & 20
\end{array}$$
-Using the adjusted winner procedure, what does Tom end up with?

Accepted Answer

A)  car and painting 
B)  car only 
C)  painting and 1/5 car 
D)  car and 3/7 painting 
A)  car and painting 
B)  car only 
C)  painting and 1/5 car 
D)  car and 3/7 painting

Question 16

Four people must make a fair division of two classic cars. They use the Knaster inheritance procedure. Their bids are shown below: $$\begin{array} { l l l l l } 
& \mathrm { A } & \mathrm { B } & \mathrm { C } & \mathrm { D } \
\text { T-Bird } & 60,000 & 90,000 & 50,000 & 50,000 \
\text { Mustang } & 70,000 & 45,000 & 100,000 & 80,000
\end{array}$$ Who gets the Mustang?

Accepted Answer

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

Question 17

Use the following information to answer the Questions:
Suppose Kim and Chris want to take turns, using the bottom-up strategy, to allocate several textbooks currently held jointly. Their ranked preferences are listed below: $$\begin{array} { | l | l | l | l | l | l | l | } 
\hline & 1 ^ { \text {st } } & 2 ^ { \text {nd } } & 3 ^ { \text {nd } } & 4 ^ { \text {th } } & 5 ^ { \text {th } } & 6 ^ { \text {th } } \
\hline \text { Chris } & \text { botany } & \text { sociology } & \text { physiology } & \text { biology } & \text { ecology } & \text { chemistry } \
\hline \text { Kim } & \text { biology } & \text { chemistry } & \text { botany } & \text { sociology } & \text { ecology } & \text { physiology } \
\hline
\end{array}$$
-If Kim chooses first, what is Chris's first choice?

Accepted Answer

A)  botany 
B)  sociology 
C)  physiology 
D)  biology 
A)  botany 
B)  sociology 
C)  physiology 
D)  biology

Question 18

Which of the following fair-division procedures is not envy-free?

Accepted Answer

A)  adjusted winner procedure 
B)  Knaster inheritance procedure 
C)  last-diminisher method 
D)  divide-and-choose 
A)  adjusted winner procedure 
B)  Knaster inheritance procedure 
C)  last-diminisher method 
D)  divide-and-choose

Question 19

Use the following information to answer the Questions
At the end of the lease on their apartment, Abe and Bonnie decide to rent separate places and so must make a fair division of the property they purchased together. The items to be divided and the point values each person places on them are given below. $$\begin{array} { l l l } 
\text { Item } & \text { Abe's points } & \text { Bonnie's point } \
\text { Plant } & 10 & 10 \
\text { Bookcase } & 40 & 30 \
\text { Quilt } & 25 & 20 \
\text { Picture } & 25 & 40
\end{array}$$
-If Abe and Bonnie use the adjusted winner procedure to divide the property, what will Bonnie end with?

Accepted Answer

A)  plant, picture, and 1/3 quilt 
B)  picture only 
C)  plant and picture only 
D)  plant, quilt, and 1/3 picture 
A)  plant, picture, and 1/3 quilt 
B)  picture only 
C)  plant and picture only 
D)  plant, quilt, and 1/3 picture

Question 20

Two people inherit a painting. If their monetary bids on the painting are $12,560 and $9750, what is the fair distribution arrived at by the Knaster inheritance procedure?

Accepted Answer

The first person rec

What does Dana have at the end of the process?

Andi, Chris, and Kim must make a fair division of a car left to them by their father. Using the Knaster inheritance procedure, the values they bid on the car are given below. Find the results of the fair division. Andi Chris Kim Car \ 2400 \ 3000 \ 2700

What is the net value to Brook of her inheritance?

Does Ashley get more than one quarter of what she thinks the inheritance is worth?

What is the name of the fair-division procedure where one party divides the object into two parts in any way that he desires, and the other party chooses whichever part she wants?

Four people must make a fair division of two classic cars. They use the Knaster inheritance procedure. Their bids are shown below: T-Bird 60,000 90,000 50,000 50,000 Mustang 70,000 45,000 100,000 80,000 Who gets the Mustang?

Which of the following fair-division procedures is not envy-free?

Two people inherit a painting. If their monetary bids on the painting are $12,560 and $9750, what is the fair distribution arrived at by the Knaster inheritance procedure?

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Electing the President

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Exam 13: Fair Division

What does Dana have at the end of the process?

Andi, Chris, and Kim must make a fair division of a car left to them by their father. Using the Knaster inheritance procedure, the values they bid on the car are given below. Find the results of the fair division. Andi Chris Kim Car \ 2400 \ 3000 \ 2700

What is the net value to Brook of her inheritance?

Does Ashley get more than one quarter of what she thinks the inheritance is worth?

What is the name of the fair-division procedure where one party divides the object into two parts in any way that he desires, and the other party chooses whichever part she wants?

Four people must make a fair division of two classic cars. They use the Knaster inheritance procedure. Their bids are shown below: T-Bird 60,000 90,000 50,000 50,000 Mustang 70,000 45,000 100,000 80,000 Who gets the Mustang?

Which of the following fair-division procedures is not envy-free?

Two people inherit a painting. If their monetary bids on the painting are $12,560 and $9750, what is the fair distribution arrived at by the Knaster inheritance procedure?

Urban Services

Business Efficiency

Planning and Scheduling

Linear Programming

Exploring Data: Distributions

Exploring Data: Relationships

Data for Decisions

Probability: the Mathematics of Chance

Social Choice: the Impossible Dream

The Manipulability of Voting Systems

Weighted Voting Systems

Electing the President

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

Filters