Geometry of Efficient Fair Division

The fundamental solution to fair division between two people has been known for thousands of years since the days of Abraham and Lot and Hesiod: one divides and the other chooses. Barbanel (mathematics, Union College) presents a number of schemes that generalize from that solution to provide a finite constructive procedure by which a group of people-players in his terminology-can allocate something-a cake-among themselves in such a way that each has a strategy that ensures their own satisfaction even in the face of a conspiracy by all of the others. Recent philosophical and economic treatments of the problem are overtly normative, but even this mathematical approach is not completely devoid of value judgment.