Fair Division: From Cake-Cutting to Dispute Resolution

In a democracy, the problem of fair division of goods is fundamental. It is, for example, what's lurking behind contemporary discussions of affirmative action, divorce law, and even of Medicare and Social Security. Its flip-side problem--burden-sharing--which is implicated in such issues as taxation and the draft, is likewise central. The authors, one a political scientist, the other a mathematician, start with an analysis of the well-known cake-cutting paradigm of "I cut, you choose" and gradually soup it up into a model capable of accommodating situations in which there are more than two parties, or more than one good. They emphasize division procedures that are not only proportional (that give each of n claimants a 1/n share of the good), but that also have the psychological property of being "envy-free"; that is, producing allocations in which each participant thinks (often wrongly, obviously) that he received the largest portion.