Compensation and sacrifice in the probabilistic rationing of indivisible units

Abstract: We consider the problem of randomly allocating indivisible units of a resource among agents with conflicting claims on the resource. In the two-agent case, we characterize three focal rules combining axioms reflecting principles of compensation and sacrifice: probabilistic uniform awards, probabilistic uniform losses and probabilistic concede-and-divide. In the general case of n agents, the two uniform rules are characterized adding the axiom of consistency. There is, however, no consistent extension of probabilistic concede-and-divide.