Divide-and-choose is envy-free in the following sense: each of the two partners can act in a way that guarantees that, according to their own subjective taste, their allocated share is at least as valuable as the other share, regardless of what the other partner does.
Here is how each partner can act:. To an external viewer, the division might seem unfair, but to the two involved partners, the division is fair - no partner envies the other. This is because, with additive valuations, every envy-free division is also proportional. The protocol works both for dividing a desirable resource as in fair cake-cutting and for dividing an undesirable resource as in chore division.
Divide and choose assumes the parties have equal entitlements and wish to decide the division themselves or use mediation rather than arbitration. The goods are assumed to be divisible in any way, but each party may value the bits differently.
The cutter 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. The divide and choose method does not guarantee each person gets exactly half the cake by their own valuations, and so is not an exact division.
There is no finite procedure for exact division but it can be done using two moving knives ; see Austin moving-knife procedure.
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 safe 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. It is entirely possible that Bob, in his ignorance, would put all the vanilla and some amount of chocolate in one larger portion, so Carol gets everything she wants while he would receive less than what he could have gotten by negotiating.
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If Bob knew Carol's preference and liked her, 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. On the other hand, if he doesn't like Carol he can cut the cake into slightly more than half vanilla in one portion and the rest of the vanilla and all the chocolate in the other.
Carol might also be motivated to take the portion with the chocolate to spite Bob. There is a procedure to solve even this but it is very unstable in the face of a small error in judgement. At KPMG, our goal is not to be the biggest professional services firm. Our goal is to be the best professional services firm.
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