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:

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Thus, from the $150,000 kitty, a total of is withdrawn, and each of the four heirs now feels that he or she has the equivalent of one-fourth of the estate.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:

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:

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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 thus, from the $67,500 kitty, a total of is withdrawn.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:

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:

Putting the three separate analyses (house, cabin, and boat) together, we get a final settlement of