Fair Division with Uncertain Needs

Imagine that agents have uncertain needs and a resource must be divided before uncertainty resolves. In this situation, waste typically occurs when the assignment to an agent turns out to exceed his realized need. How should the resource be divided in the face of possible waste? This is a question out of the scope of the existing rationing literature. Our main axiom to address the issue is no domination. It requires that no agent receive more of the resource than another while producing a larger expected waste, unless the other agent has been fully compensated. Together with conditional strict endowment monotonicity, consistency, and strong upper composition, we characterize a class of rules which we call expected-waste constrained uniform gains rules. Such a rule is associated with a function that aggregates the two components of cost generated by an agent at an allocation: the amount of the resource assigned to him and the expected waste he generates. The rule selects the allocation that equalizes as much as possible the cost generated by each agent. Moreover, we characterize the subclasses of rules associated with homothetic and linear cost functions. Lastly, to appreciate the role of no domination, we establish all the characterizations with a decomposition of no domination into two axioms: risk aversion and no reversal. They respectively capture that a rule should not ignore the claim uncertainty, and neither should it be too sensitive to the claim uncertainty.