Math assignment: Fair Division
by Macie Wilkins.
Knaster Inheritance Procedure
The Knaster Inheritance Procedure allows for more than 2
parties and for assets which cannot be divided. Here's an
example if Carrie bids $28,225 and Marti bids $32,100 on
their aging parents car. The bigger bitter obviously should
get the car. But the winner has to pay out the loser a fair share.
The highest bidder places $16,050 into a "kitty"; and the
loosing heir gets to withdraw 1/2 of the value he bid. This
leaves 1937.50 in the kitty and thats distributed to both of
them. In result at the end Marti gets the car plus $968.75.
Carrie gets $968.75 plus $14,112.50.
Definition of last-dimisher method-The last diminisher procedure is a procedure for
fair cake-cutting. It involves a certain heterogeneous and divisible resource,
such as a birthday cake, and n partners with different preferences over different
parts of the cake. It allows the n people to achieve a proportional division, i.e.,
divide the cake among them such that person receives a piece with a value of at
least 1/n of the total value according to his own subjective valuation.
Last-Diminisher method Lets say 4 salespeople are dividing
a state in four sales regions. They pull names from a hat to
decide play order. The first person picks a piece they like
then the next person states if he thinks its more or less than a
fair share. If they say its fair it stays the same if they say its
more than fair the amount of state is trimmed. If that person
trims it then that's their land now. The first person that
originally chose the first piece must chose another for
themselves. The last person gets the benefit because they
could just slightly trim the land and claim it four themselves.
So their first choices second choice has been taken. Now since
their are only two people left they did divider achievement.
So they flip a coin then the winner of that chooses the land they
want and the loser of the coin flip gets the left over land.
Taking turns is one of the simplest methods because it only involves two people and
distributing things equally. Say you have Cletus and Margret. They are getting a
divorce and have 4 large items they want to distribute. A mini van, their family
dog taco, a sports car and a freezer. They are given 100 points are they are asked
to rate the items with points on representing how important they are to them.
Cletus put 10 on the mini van, 20 on the family dog, 40 on the sports care and 30
for the freezer. Margaret put 40 on the mini van, 45 on the family dog, 5 on the
sports car and 10 on the freezer. In this problem you could tell who like what so
Cletus would end up getting the sports car and the freezer.
Margaret would get the mini van and the family dog.