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Chapter 14 – Fair Division

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Chapter 14 – Fair Division

Part 2: The Knaster Inheritance Procedure

- We could use the adjusted winner procedure if an inheritance was to be divided among two heirs.
- The Knaster Inheritance Procedure provides a means of dividing up items (such as an estate inheritance) among two or more interested parties.
- The Knaster Inheritance Procedure does have the following drawback: One or more parties may need to provide a large amount of cash to reach an agreement.

- Example #1: Suppose four individuals (Bob, Carol, Ted and Alice) have equal claim to an inheritance consisting of a house, a cabin and a boat. Because there are four individuals and three items, and the items are not equally valued, these individuals could use the Knaster Inheritance procedure to negotiate a division of the estate.
- This procedure will proceed one item at a time, deciding who will get which item. The individual who does not receive any item will be compensated in cash, and those who receive items of lesser value will also be compensated, in cash, by those who receive items of greater value.
- Let’s begin this example by considering the house …

- Each party to the negotiation will make a bid on the house. Suppose the bids are as follows …
- Carol is the highest bidder and therefore will receive the house. However, the others will be compensated, in cash, by Carol.
- This is done as follows: It was a given assumption at the outset of the negotiations that all participants have equal claim to all of the items and to this house, in particular. Thus, in a sense, Carol has a claim to 1/4 of the house, which she values to be (1/4)($200,000) = $50,000.

- Because Carol only has a fair claim to 1/4th of the house, she will compensate the others by paying the remaining 3/4th of her estimate of its’ value, which is (3/4)($200,000) = $150,000 into a temporary account (sometimes called a “kitty”).
- Each of the other parties now withdraw 1/4th of what they estimate as the value of the house. Therefore the following initial distributions are made:
- Bob: (1/4)(his estimate) = (1/4)(120,000) = $30,000
- Ted: (1/4)(his estimate) = (1/4)(140,000) = $35,000
- Alice: (1/4)(her estimate) = (1/4)(180,000) = $45,000.

- Note that $30,000 + $35,000 + $45,000 = $110,000 which means there is a surplus of $40,000 in the temporary account. That surplus is equally divided among the four individuals (including Carol)

- Because the surplus in the temporary account was $40,000, each party gets (1/4)($40,000) = $10,000.
- The conclusion with respect to the house is as follows:
- Carol: gets the house and pays $140,000. (She got back $10,000)
- Bob: gets $30,000 + $10,000 = $40,000.
- Ted: gets $35,000 + $10,000 = $45,000.
- Alice: gets $45,000 + $10,000 = $55,000.

- Each party receives more than 1/4th of what they perceive as the value of the house. Clearly, from the point of view of either Bob or Ted, this procedure does motivate the individuals toward an agreement over the value of the house.
- Notice however, that if they all valued the house equally, then the Knaster Inheritance Procedure would be undecided as to who to award the house. To be awarded the house, one party would need to outbid the others.

- Because there were other items to be divided among these individuals, using the Knaster Inheritance Procedure to distribute them, we continue with each item, applying the same procedure for each item …
- Because we are not done, we can consider each of those cash distributions related to the decision on the house to be temporary. For example, any of the other parties may be paying for receipt of the next item. For this reason, no cash need change hands until all of the calculations are done regarding all of the items.

- Suppose the four individuals make the following bids on the cabin and boat:
- We proceed as before, one item at a time, calculating the amounts for the temporary accounts and corresponding distributions.
- Let’s consider the cabin next.

- Ted outbids the others on the cabin and therefore is awarded the cabin.
- However, Ted initially has claim to only 1/4th of the cabin and therefore has to pay the others to receive their share of the cabin.
- Therefore Ted will pay (3/4)($90,000) = $67,500 for the cabin into a temporary account.

- Now, in compensation for their portion of the cabin,
- Bob receives (1/4)($60,000) = $15,000
- Carol receives (1/4)($40,000) = $10,000
- Alice receives (1/4)($50,000) = $12,500

- Finally, because $15,000 + $10,000 + $12,500 = $37,500 there still remains $67,500 – $37,500 = $30,000 in the temporary account.
- This surplus $30,000 is distributed equally among allfour parties. Thus each will get $7,500.

- The result of the negotiations on the cabin are as follows:
- Ted: Gets the cabin and pays $60,000 (he got back $7500)
- Bob: Receives $15,000 + $7,500 = $22,500
- Carol: Receives $10,000 + $7,500 = $17,500
- Alice: Receives $12,500 + $7,500 = $20,000

- Finally, we consider the boat.
- Bob outbids the others and is awarded the boat. He will pay (3/4)($30,000) = $22,500 for the boat into a temporary account.
- The others withdraw 1/4th of their estimate of the value of the boat.
- Carol receives (1/4)($24,000) = $6,000
- Ted receives (1/4)($20,000) = $5,000
- Alice receive (1/4)($20,000) = $5,000

- The conclusion with regards to the boat is as follows.
- There is a surplus in the temporary account of $22,500 – $16,000 = $6,500. This is distributed equally among all four participants which means each receives $1,625 from the surplus in the temporary account.

- The final distributions (regarding the boat) are:
- Bob gets the boat and pays $20,875 (he received $1625 back)
- Carol receives $6,000 + $1625 = $7,625.
- Ted receives $5,000 + $1625 = $6,625.
- Alice receive $5,000 + $1625 = $6,625.

- These were the original bids from the four participants. We may now consider how each faired in the overall negotiation.
- The Knaster inheritance procedure can be used to divide any number of goods among any number of individuals. It will not be necessary to divide any one item among individuals.
- A drawback is that each individual may need to bring some other assets (like cash) to the negotiations. Essentially, this method takes advantage of differences in the individuals’ valuations of the items and provides a way for each to buy the others’ claims to an equal share of the items.

- Looking back over each calculation, we can now account for all of the transactions.
- In this way, we do not actually need to make all of the transactions. We can simply calculate the net balances for each individual.
- In this example, we find the following transactions were calculated:

- Thus, based on these initial valuations, the final result is as follows:
- Bob gets the boat and receives $41,625
- Carol gets the house and pays $114,875
- Ted gets the cabin and pays $8,375
- Alice receives $81,625.

- The property has been divided among the individuals and each participant receives more than 1/4th (their fair share) of the value they placed on the items.