What is Fair Division?

Legal Definition
Fair division is the problem of dividing a set of goods or resources between several people who have an entitlement to them, such that each person receives his/her due share. This problem arises in various real-world settings: auctions, divorce settlements, electronic spectrum and frequency allocation, airport traffic management, or exploitation of Earth Observation Satellites. This is an active research area in Mathematics, Economics (especially Social choice theory), Game theory, Dispute resolution, and more. The central tenet of fair division is that such a division should be performed by the players themselves, maybe using a mediator but certainly not an arbiter as only the players really know how they value the goods.

There are many different kinds of fair division problems, depending on the nature of goods to divide, the criteria for fairness, the nature of the players and their preferences, and other criteria for evaluating the quality of the division.

The mathematical fair division problem is an idealization of those real life problems. The theory of fair division provides explicit criteria for various different types of fairness. Its aim is to provide procedures (algorithms) to achieve a fair division, or prove their impossibility, and study the properties of such divisions both in theory and in real life.
-- Wikipedia