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. An axiom reflecting a principle of compensation allows us to characterize the focal probabilistic uniform awards rule. A dual axiom reflecting a principle of sacrifice allows us to characterize the (dual) probabilistic uniform losses rule. The combination of two (other) axioms reflecting both principles (of compensation and sacrifice) allows us to characterize the (compromise) probabilistic concede-and-divide in the two-agent case. There is, however, no consistent extension of this rule to the general case of an arbitrary number of agents.