There are three properties of the adjusted winner allocation that are important.
1) The allocation is equitable (each player believes that he or she receives the same fractional part of the total value).
2) The allocation is envy­free (each player gets a share of whatever is being divided that is at least as large, or at least as desirable, as that received by any other player).
3) The allocation is Pareto­optimal (no other allocation achieved by any means can make one player better off without making some other player worse off).
The drawback of the Adjusted Winner Procedure is that it only works in distributions involving two parties. If we have three or four heirs trying to divide property or goods left by their parents, we need to turn to another procedure, discussed in the next section.
13.2 The Knaster Inheritance Procedure The Knaster Inheritance procedure was first proposed by Bronislaw Knaster in 1945. The major drawback of this procedure is that it requires the heirs to have a large amount of cash at their disposal. The advantages of this procedure are that it works for more than two parties, and that each party ends up getting more than what they believe is a fair share! 1
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Consider the following situation, in which three siblings are interested in a house that their parents have left them.
Example 1 (Dividing one item among 3 people)
Joe, Mary, and Ted inherit a house. Their respective bids on the house are $90,000, $60,000, and $75,000. Find a fair division using the Knaster Inheritance Procedure.
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Example 2 (Dividing two items among 3 people)
Bill, Clark, and Dean inherit an apartment in Manhattan and a cottage on Cape Cod. Their respective bids are shown in the table below. Find a fair division using the Knaster Inheritance Procedure.
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Example 3 Bob, Carol, and Doug must divide a cabin, some silver, and a car using the Knaster Inheritance Procedure. Their bids are in the following table. Find the final division.
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Example 4 Sam and Pat inherited several items from a great­aunt and must divide them. Their bids are in the following table. Use the Knaster Inheritance Procedure to find a fair allocation.
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Homework: Read section 13.2 and do HW #16. 7