Fair Division Algorithms and Experiments: A Short Review

We concisely review established and recent results regarding procedures to allocate several objects (also referred to as items or goods) to a finite number of entities (usually denotes as agents or players). After having described how to formally represent preferences, and what defines a good allocation, we list the procedures. For each procedure we outline the assumptions, the terminology specifically employed for the occasion, and the results achieved, together with specific remarks for the examined procedure. Our analysis reveals that some procedures are mature enough to guarantee a reasonable degree of success in the legal context. Some others are very recent, but their strong theoretical grounds provide a natural perspective of applications in the legal context. Behavioral and experimental economics provides rigorous evidence of the effectiveness of these procedures and the perception of those among the involved agents.