The adjusted winner procedure can be applied in the case of an inheritance if there are only two heirs. For more than two heirs, there is quite a different scheme: the Knaster inheritance procedure, first proposed by Bronislaw Knaster in 1945. It has a drawback, though, in that it requires the heirs to have a large amount of cash at their disposal.
EXAMPLE 1 A Four-Person Inheritance
Suppose (for the moment) that there is just one object—a house—and four heirs—Bob, Carol, Ted, and Alice. Knaster’s scheme begins with each heir bidding (simultaneously and independently) on the house. Assume, for example, that the bids are as follows:
| Bob | Carol | Ted | Alice |
|---|---|---|---|
| $120,000 | $200,000 | $140,000 | $180,000 |
Carol, being the high bidder, is awarded the house. Her fair share, however, is only one-fourth of the $200,000 she thinks the house is worth, and so she places $150,000 (which is three-fourths of the $200,000 she bid) into a temporary “kitty.”
Each of the other heirs now withdraws from the kitty his or her fair share—that is, one-fourth of his or her bid.
Thus, from the $150,000 kitty, a total of is withdrawn, and each of the four heirs now feels that he or she has the equivalent of one-fourth of the estate. Moreover, there is a $40,000 surplus , which is now divided equally among the four heirs (so each receives an additional $10,000). The final settlement is as follows:
| Bob | Carol | Ted | Alice |
|---|---|---|---|
| $40,000 | House – $140,000 | $45,000 | $55,000 |
This illustrates Knaster’s procedure for the simple case in which there is only one object. But what if our same four heirs have to divide an estate consisting of (say) a house (as before), a cabin, and a boat? There are actually two ways to handle this situation, and we’ll illustrate both, assuming that our four heirs submit the following bids:
| Bob | Carol | Ted | Alice | |
|---|---|---|---|---|
| House | $120,000 | $200,000 | $140,000 | $180,000 |
| Cabin | $60,000 | $40,000 | $90,000 | $50,000 |
| Boat | $30,000 | $24,000 | $20,000 | $20,000 |
545
The first way to deal with the situation is simply to handle the estate one object at a time, proceeding for each object as we just did for the house. We have already settled the house. Let’s handle the cabin the same way. thus, ted is awarded the cabin based on his high bid of $90,000. His fair share is one-fourth of this, so he places three-fourths of $90,000 (which is $67,500) into the kitty.
Bob withdraws from the kitty . Carol withdraws , and Alice withdraws . thus, from the $67,500 kitty, a total of is withdrawn. the surplus left in the kitty is $30,000, and this is again split equally ($7500 each) among the four heirs. the final settlement on the cabin is as follows:
| Bob | Carol | Ted | Alice |
|---|---|---|---|
| $22,500 | $17,500 | Cabin – $60,000 | $20,000 |
If we were now to do the same for the boat (we leave the details to you), the corresponding final settlement would be as follows:
| Bob | Carol | Ted | Alice |
|---|---|---|---|
| Boat – $20,875 | $7625 | $6625 | $6625 |
Putting the three separate analyses (house, cabin, and boat) together, we get a final settlement of
Notice that in this situation Carol gets the house but must pay $114,875 in cash (and Ted gets the cabin but must put up $8375 in cash). This cash is then disbursed to Bob and Alice. In practice, Carol’s having this amount of cash available may be a real problem—the key drawback to Knaster’s procedure. Nevertheless, Knaster’s procedure shows again that whenever some participants have different evaluations of some objects, there is an allocation in which everyone obtains more than what they would normally consider a fair share.
EXAMPLE 2 Another Way
The second way begins by adding two rows to the chart of bids, one giving the total value of the estate to each heir (arrived at by summing the columns) and the other giving each heir’s fair share (which is one-fourth the value of the estate because there are four heirs).
| Bob | Carol | Ted | Alice | |
|---|---|---|---|---|
| House | $120,000 | $200,000 | $140,000 | $180,000 |
| Cabin | $60,000 | $40,000 | $90,000 | $50,000 |
| Boat | $30,000 | $24,000 | $20,000 | $20,000 |
| Total value | $210,000 | $264,000 | $250,000 | $250,000 |
| Fair share | $52,500 | $66,000 | $62,500 | $62,500 |
546
Next, we give each item to the party who values it most. Bob gets the boat, Carol gets the house, and Ted gets the cabin. This is certainly not fair because Carol got the most valuable item and Alice got nothing. We fix this in the following way:
At this point, every party has his or her fair share. However, the estate has taken in more than it has paid out. This is called the surplus.
We now divide the surplus evenly among the parties.
Finally, we give an additional $19,125 to each party, making the final division (as before) the following:
Bob gets the boat and .
Carol gets the house and pays the estate .
Ted gets the cabin and pays the estate .
Alice gets $81,625 cash .
We summarize Knaster’s inheritance procedure as follows.
Basic Steps in Knaster’s Inheritance Procedure with Heirs PROCEDURE
For each object, the following steps are performed: