Entitlement (fair division)

Entitlement in fair division describes that proportion of the resources or goods to be divided that a player can expect to receive. In many fair division settings, all agents have equal entitlements, which means that each agent is entitled to 1/n of the resource. But there are practical settings in which agents have different entitlements. Some examples are:

• In partnership resolution settings, each partner is entitled to a fraction of the common assets in proportion to his/her investment in the partnership.
• In inheritance settings, the law in some jurisdictions prescribes a different share to each heir according to his/her proximity to the deceased person. For example, according to the Bible, the firstborn son must receive twice as much as every other son. In contrast, according to the Italian law, when there are three heirs - parent, brother and spouse - they are entitled to 1/4, 1/12 and 2/3 respectively.
• In parliamentary democracies, each party is entitled to a number of seats in the parliament that is, in general, proportional to the number of votes it received.

The idea is based on the normal idea of entitlement. Entitlements can be determined by agreeing on a cooperative game and using its value as the entitlement.

When agents have equal entitlements, it is reasonable to require that the solution satisfies the axiom of anonymity (also called: symmetry), that is, agents are treated only by their valuations and not by their names. In contrast, when agents have different entitlements, anonymity is no longer valid, and the solutions must be asymmetric.

Various problems of fair division with different entitlements have been studied.