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## + - An Envy-Free Algorithm ->

Submitted by mikejuk
mikejuk (1801200) writes "If you want to find a way of dividing up some indivisible items between entities then here is a way to do it that eliminates envy as the outcome. The suggestion is that this could be a good way to divide up possessions during a divorce — algorithms get into everything. A new paper (http://www.ams.org/notices/201402/rnoti-p130.pdf) by New York University’s Steven Brams, Wilfrid Laurier University’s D. Marc Kilgour, and the University of Graz’s Christian Klamler and published this month in Notices of the American Mathematical Society, outlines how to do it so that both parties are happy in a maximal sort of way — i.e it assigns as many items in the pool of things to be divided and only holds back those that if allocated would cause envy.
As long as the players assign true rankings to the items then the more algorithm will find the maximal envy-free assignment and as the number of items increases, the probability of a complete envy-free assignment approaches one.
The bad news is that you can cheat.
If you lie about your ranking you can end up with an assignment that, when you true ranking is revealed, provokes envy. However, as the authors note the danger is that you won't work things out perfectly, because it depends on the ranking of the other player and you could end up worse off. The best strategy is to play fair and end up with an envy free allocation.
So the next time you file for divorce, remember to hire a programmer as well as a lawyer."