fair division lone divider and chooser
TRANSCRIPT
What if there is more than two players?
we'll look at three different solutions:
1. The lone-divider method
2. The lone-chooser method
3. The last-diminisher method
One person is the divider, chosen randomly. The remaining players "bid" on which of the pieces cut by the divider are fair shares. The pieces are then separated into two groups: the "bid for" and the "unbid for"
Case 1: The "bid for" group has two or more pieces in it. Give each
chooser the piece they bid on and the divider the last remaining piece.
Case 2: There is only one piece in the "bid for' group. Combine this one
piece with one of the "unbid for" pieces. The remaining piece goes to the divider. The new piece is then divided using the divider- chooser method.
1. The lone-divider method --
Case 1: The "bid for" group has two or more pieces in it. Give each
chooser the piece they bid on and the divider the last
remaining piece.
Bid For:
Un-bid For:
s1
s2
s3
Hector TheoLarry
Case 2: There is only one piece in the "bid for' group. Combine this one
piece with one of the "unbid for" pieces. The remaining piece goes to the divider. The new piece is then divided using the divider-chooser method.
Bid For:
Un-bid For:
s1 s2
s3
Hector Theo Larry
Hector Theo
Larry
s3
Bid For:
s1 Un-bid For:
s2
s 1 s 2 s 3
Hector 33.3% 33.3% 33.3%
Theo 35% 10% 55%
Larry 40% 25% 35%
Example #2
Larry
Theo
Hector
s 1 s 2 s 3
Theo 33.3% 33.3% 33.3%
Hector 20% 30% 50%
Larry 10% 20% 70%
Hector
Theo
Larry
1. The lone-divider method --
Example #3
Hector
Larry
Theo
In Honor of Grandpa: Land DivisionUsing the Lone-Divider MethodLand Value=$200,000
Hector
Larry
Theo
Lisa
fair share value=
Theo
$35K$60K
$50K
$55K
Hector
$10K $15K
$105K
$70K
Larry
$60K
$35K
$65K
$40K
Lisa
$50K$50K
$50K
$50K
Hector
Larry
Theo
Lisa
Homework: p. 99 #11, 12, 15, 19
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