Fair Division Practice #3
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Name:_____________________________ #
Consider a fair division problem involving 5 players. The phrase “a player receives a fair share” describes the fact that:
a) The player receives a share that is at least as valuable as that of any other player.
b) The player receives a share that is more valuable than that of any other player.
c) The player receives a share that, in the player’s opinion, has value that is equal to 20% or more of the total.
d) The player receives a share that, in the player’s opinion, has value that is exactly equal to 20% of the total.
e) None of the above.
An estate consisting of a car, a boat, a house, some cash and a diamond ring must be divided fairly among five heirs. This
type of problem is called:
a) A continuous fair division problem.
b) A discrete fair division problem.
c) A mixed fair division problem.
d) The method of sealed bids.
e) None of the above.
Which of the following is a discrete fair division problem?
a) Dividing a gallon of ice cream
b) Dividing a tropical island
c) Dividing a cheese pizza
d) Dividing an antique car collection
e) None of the above
Questions 4 and 5 refer to the following situation: Three players (Tiffany, Paxton and Sandra; Paxton is the divider and Tiffany and
Sandra are the choosers) are going to divide a cookie (a large one!) fairly using the lone divider method. Paxton cuts the cookie into
three slices:
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s1 , s 2 , s3 .
If the choosers declarations are Sandra:
a)
b)
c)
d)
e)
s2 and Tiffany: s 3 , which of the following is a fair division of the cookie?
Sandra gets s1; Tiffany gets s2; Paxton gets s3.
Sandra gets s3; Tiffany gets s2; Paxton gets s1.
Sandra gets s2; Tiffany gets s3; Paxton gets s1.
Sandra gets s2; Tiffany gets s1; Paxton gets s3.
None of the above.
5.
If the choosers declarations are Sandra: s2 and Tiffany s1, s2, which of the following is a fair division of the cookie?
a) Sandra gets s2; Tiffany gets s1; Paxton gets s3.
b) Sandra gets s2; Tiffany gets s3; Paxton gets s1.
c) Sandra gets s3; Tiffany gets s1; Paxton gets s2.
d) Sandra and Tiffany split s2; Paxton gets s1 and s3.
e) None of the above.
6.
Ann and Betsy buy a ½ mint chocolate, ½ strawberry mousse cake for $12. Ann values mint chocolate three times as much
as she values strawberry. Betsy values both kinds equally.
a) What is the value of the mint chocolate half of the cake to Ann?
b) What is the value of the strawberry half of the cake to Ann?
c) Betsy cuts the cake without paying attention to whether the parts are mint chocolate or strawberry. One of the pieces
she cuts is 40° mint chocolate and 60° strawberry. What is the value of that piece to Ann?
7.
Jody does not comparison shop before she buys a similar cake for $13.50. Jody values strawberry four times as much as she
values mint chocolate.
a) What is the value of the mint chocolate half of the cake to Jody?
b) What is the value of the strawberry half of the cake to Jody?
c) What would Jody value a piece of cake that was is 40° mint chocolate and 60° strawberry?
8.
Four partners (Adams, Benson, Cagle, and Duncan) jointly own a piece of land. The land is subdivided into four parcels
s1 , s 2 , s3 , s 4 . The following table shows the relative value of the parcels (as a percentage of the value of the land) in the
eyes of each partner.
Adams
Benson
Cagle
Duncan
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s1
s2
s3
s4
30%
35%
25%
20%
24%
25%
15%
20%
20%
20%
40%
20%
26%
20%
20%
40%
a) Indicate which of the four parcels are fair shares to Adams.
b) Indicate which of the four parcels are fair shares to Benson.
c) Indicate which of the four parcels are fair shares to Cagle.
d) Indicate which of the four parcels are fair shares to Duncan.
e) Assuming that the four parcels cannot be changed or further subdivided, describe a fair division of the land.
Three players are going to divide a cake fairly using the lone chooser method. Using this method
a) The first division consists of dividing the cake into 2 pieces , the second division consists of dividing each of these pieces
into 2 pieces.
b) The first division consists of dividing the cake into 3 pieces, the second division consists of dividing each of these pieces
into 2 pieces.
c) The first division consists of dividing the cake into 2 pieces, the second division consists of dividing each of these pieces
into 3 pieces.
d) The first division consists of dividing the cake into 3 pieces, the second division consists of dividing each of these pieces
into 3 pieces.
e) None of the above.
Questions 10 through 13 refer to the following situations: Five players agree to divide a cake fairly using the last diminisher method.
The players play in the following order: Amber first, Demetrius second, Shanni third, Sherrie fourth, and Stacy last. Suppose that
there are no diminishers in round 1 and Shanni and Sherrie are the only diminishers in round 2.
10. Which player gets their fair share at the end of round 1?
a) Amber
b) Demetrius
c) Shanni
d) Sherrie
11. Which player is the first to cut the cake at the beginning of round 2?
a) Amber
b) Demetrius
c) Shanni
d) Sherrie
12. Which player gets their fair share at the end of round 2?
a) Amber
b) Demetrius
c) Shanni
d) Sherrie
13. Which player is the first to cut the cake at the beginning of round 3?
a) Amber
b) Demetrius
c) Shanni
d) Sherrie
14. Describe an envy-free method of dividing a cake among four people.
15. Is the divider-chooser method an envy-free method? Explain.
e) Stacy
e) Stacy
e) Stacy
e) Stacy