Divide and choose

From Wikipedia, the free encyclopedia

In problems of fair division, divide and choose (also I cut, you choose) is a method whereby two people may divide a resource in an envy-free manner.

In the method, one person divides the resource into what they believe are equal halves, and the other person chooses the "half" they prefer. Thus, the person making the division has an incentive to divide as fairly as possible: for if they do not, they will likely receive an undesirable portion. This rule is a concrete application of the veil of ignorance concept.

Analysis of the method becomes more difficult if two players place different values on some subsets of the resource. One commonly used example is a cake that is half vanilla and half chocolate. Suppose Bob likes only chocolate, and Carol only vanilla. If Bob is the cutter and he is unaware of Carol's preference, his optimal strategy is to divide the cake so that each half contains an equal amount of chocolate. But then, regardless of Carol's choice, Bob gets only half the chocolate and the allocation is clearly not Pareto efficient.

In this case, if Bob knew Carol's preference, he could cut the cake into an all-chocolate piece, and an all-vanilla piece, Carol would choose the vanilla piece, and Bob would get all the chocolate.