Name____________________________________Date_____________________Hour_______Score________
Fair Division Homework 1
1. What are 3 key elements for a Fair Division game?
2. What are the 4 assumptions made about the players?
In problems 3-6, calculate the value of a share.
3. Michael likes pepperoni twice as much as cheese.
4. Jennifer likes Coke three times as much as Pepsi.
5. Josh likes USU twice as much as BYU and likes BYU 3 times as much as the U of U.
6. A circular ice cream cake is made with 3 equal parts of Strawberry (S), Chocolate
(C), and Vanilla (V) ice cream. Mr. Smith likes Chocolate 4 times as much as
Vanilla and likes Vanilla 3 times as much as Strawberry.
7. What is the method to divide with two players?
8. Which player do you prefer to be? Why?
9. Example of divider/chooser method.
Use problem 6 to help answer problem 10.
10. A vertical cut that
horizontal
makes one piece all
strawberry and 30⁰ vanilla
and chocolate each
Problem 7
b. A
cut that makes
one piece all
chocolate and
60⁰ of strawberry
C
S
V
Cut
Problem 8
C
S
V
Cut
Name____________________________________Date_____________________Hour_______Score________
Calculate the value of the following shares to each person:
11. Greg likes red velvet cake 3 times as much as cookie cake.
Piece #1: 900 Red Velvet and 700 cookie
700
900
Red
Cookie
Velvet
600
1100
Piece #2: 1100 Cookie and 300 Red Velvet.
300
Piece #3: 600 Red Velvet
12.Jessica likes both Mint Chocolate Chip and Cookies and Cream ice cream twice as
much as vanilla and hates strawberry. Quinten likes strawberry twice as much as all
other flavors.
Piece #1: 900 Vanilla and 450 Mint Chocolate Chip
Vanilla
Mint
Chocolate
Chip
Piece #2: 450 Mint Chocolate Chip and 600 Strawberry
Cookies
and Cream Strawberry
Piece #3: 300 Strawberry and 900 Cookies and Cream
13. A 12 inch Subway sandwich contains 6 inches of Turkey and 6 inches of Roast Beef.
Suzanne cut the sandwich into two pieces with one piece containing 2 inches of
Turkey and 6 inches of the Roast Beef and the other piece is only 4 inches of Turkey.
Suppose Jordan like Turkey four times as much as Roast Beef. What are the values
that Jordan assigns to the two pieces of sandwich?
Turkey
Roast Beef
Name____________________________________Date_____________________Hour_______Score________
14. A. Suppose you liked Italian twice as much as Veggie. Would you cut in the Veggie
or Italian half to create two fair shares of the sandwich? Why?
B. Would a carnivore cut in the Veggie or Italian half to create two fair shares?
C. Would a vegetarian cut in the Veggie or Italian half to create two fair shares?
Veggie
#15.
P1
P2
P3
Italian
S1
30%
S2
40%
S3
30%
331/3%
50%
331/3%
15%
331/3%
35%
A. Who is the divider?
B. What is the bid list of each player?
C. What is the fair division of the shares?
A. Who is the divider?
B. What is the bid list of each player?
#16.
P1
P2
P3
P4
S1
45%
25%
0%
25%
S2
35%
20%
50%
25%
S3
10%
20%
40%
25%
S4
10%
35%
10%
25%
C. What is the fair division of the shares?
#17.
P1
P2
P3
P4
P5
S1
10%
25%
20%
30%
5%
S2
40%
10%
20%
15%
30%
S3
7%
35%
20%
22%
15%
S4
35%
15%
20%
13%
35%
S5
8%
15%
20%
20%
15%
A. Who is the divider?
B. What is the bid list of each player?
C. What is the fair division of the
shares?
Name____________________________________Date_____________________Hour_______Score________
18. Three partners are dividing a plot of land among themselves using the Lone
Divider method. P1 is chosen to divide the property into three parcels s1, s2, and
s3. P2 bid list is {s2} and P3 bid list is {s1, s3}. What is one fair division of the
parcels?
19. Three siblings are trying to split candy from Halloween. They decide to use
Lone-Divider Method to determine who gets what bag of candy.
Exp #2:
Sibling 1
Sibling 2
Sibling 3
Bag 1 (s1)
60%
50%
33.3%
Bag 2 (s2)
20%
23%
33.3%
Bag 3 (s3)
20%
27%
33.3%