Valentine’s Day is a good time to discuss the flaws in this “envy free” algorithm.
Researchers Develop “Envy-Free” Algorithm for Settling Disputes from Divorce to Inheritance
The headline should have read:
Researchers Develop Theoretical Algorithm for Settling Disputes from Divorce to Inheritance
From the article:
This algorithm is “envy free” because each party prefers each of its items to a corresponding item of the other party. A potential conflict arises, of course, when the two parties desire the same item at the same time. For example, assume players A and B rank four items, going from left to right, as follows:
A: 1 2 3 4
B: 2 3 4 1Now, if we give A item 1 and B item 2 (their most preferred), the next unallocated item on both their lists is item 3. Who should get it? The algorithm gives it to A and gives item 4 to B, which is an envy-free allocation because each player prefers its items to the other player’s:
A prefers item 1 to 2 and item 3 to 4
B prefers item 2 to 3 and item 4 to 1Not only does each party prefer its pair of items to the other’s, but there is no alternative allocation that both parties would prefer, which makes it efficient. Although such an efficient, envy-free allocation is not always possible, the algorithm finds one that comes as close to this ideal as can be achieved.
The first problem with the algorithm is that while it may account for envy, it does not account for the desire of party A to deprive party B of anything B desires.
Failing to account for spite, the algorithm is useful only in non-spiteful divorces and inheritance disputes.
Care to wager on the incidence of non-spiteful divorces and inheritance disputes?
Distinct from any “envy” or “spite” with regard to material items, there are other issues that the algorithm fails to account for in a divorce or inheritance dispute.
I can’t share the details but I do recall the testimony in one case being the other spouse had remarried, “that ugly woman.” That was the real driver behind all of the other issues.
The “envy-free” algorithm isn’t quite ready for a scorned spouse case.
All algorithms sound good in an ideal world. Next time you read about an algorithm, think of data that isn’t ideal for it. Become an algorithm skeptic. Your clients will be better off for it.