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# Dividing an Inheritance Three Ways

I once saw a TV movie, probably a BBC production, probably a movie version of a classic novel, a period costume drama set in England in the 1800's. It had several protagonists we were supposed to care about, and lots of soap opera. One protagonist was a man around 30 years of age, a minor relative of a wealthy family who had never been successful himself. Due to a tragedy, the major members of this family had died, and the whole estate was going to be divided among the more distant relatives. This young man became obsessed with getting his fair share, but the other heirs disputed his claim, so the case went to court. The case dragged on for years, and every heir had at least one lawyer, some had more. The young man became even more obsessed, and hired a more expensive lawyer. There finally came a day when the judge was ready to announce a decision. The lawyer's fees had consumed the entire value of the estate, so the case was now moot, and was dismissed. Our hopeful young man died of a heart attack on the courtroom floor.

I studied economics for too many years, and it happens that economists have a formula to use for dividing an inheritance fairly. Inheritances are often "mixed goods", some cash, some real estate, some tools, some livestock, some stocks and bonds, some jewelry, some items of purely sentimental value. Different heirs value these goods differently. One might strongly want a house, while another might consider the same house a burden. One might be able to use the tools while another would not. How to divide such mixed goods?

If you have two heirs, A and B, the formula is simple. Let A divide the inheritance into two bundles, of equal value in A's opinion, so that A is truly indifferent as to which of them A gets. B gets first pick.

What if you have three heirs, A, B, and C?
(1) A divides the estate into three bundles, of equal value in A's opinion, so that A is truly indifferent as to which of them A gets.
(2) B then has the option of trimming off part of one of the bundles, so that the two best bundles, in B's opinion, are equally good. The trimmings are set aside to be handled later.
(3) C gets first pick.
(4) B gets second pick, except that IF the bundle that B trimmed is still on the table, B must get that one. Notice that B is thus guaranteed to get one of the "two best that are equal in B's opinion".
(5) A gets the remaining bundle. Notice that A is thus guaranteed to get one of the untrimmed bundles, which A judged to be equally as good as the others.
(6) The trimmings are then put back on the table, and the process starts again at step (1) above. This continues until the trimmings are too small to bother with.

There are analogous formulae for 4, 5, 6, etc. heirs, but they become exponentially more complex.

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Comment by James M. Martin on March 8, 2013 at 7:29pm

Come again?

Comment by John B Hodges on March 8, 2013 at 12:45pm

To Joan- I'm afraid I've not heard of an actual case, this is just a mental puzzle solved, the way theoretical economists do.
To Randall- Look into TRUSTS. In our family we learned about this some years back; we set up the "Hodges Family Trust", and the parents put all of their assets into the trust, (except for a couple that they just plain forgot about). The rules of the trust specify who has decision-making authority to manage the assets in the trust; Dad, then Mother, then the three kids acting jointly. The point of this is to avoid Probate, which can take a long time and involve lots of lawyer fees. Dad died recently, Mother is in failing health, and I wrote the above as a letter to my sisters who are having some disputes. Dad also had a will; I understand that's good to have even if you also have a Trust. To get the benefit of quick and inexpensive process of inheritance, you have to set up the trust BEFORE you die, and you have to put your assets IN the trust. So definitely, see the lawyer, update the will, and look into setting up a trust.
I'm hardly an expert on this stuff; the above is about all I have to say.

Comment by Randall Smith on March 8, 2013 at 7:46am
Quite apropos for me at this time: 95 year old father, 3 children. I just yesterday asked him if he knew what was in his will. Answer: NO. I said, "we need to talk and see the lawyer". His assets are complicated, and I am concerned about the outcome. I like your formula.
Comment by Joan Denoo on March 8, 2013 at 12:31am

Have you found this formula works to the satisfaction of three or more? The division for two sounds like a process a wise mother uses to divide up a cake.

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