Equal-quantile rules in resource allocation with uncertain needs

A group of agents have uncertain needs on a resource, which must be allocated before uncertainty re-solves. We propose a parametric class of division rules we call equal-quantile rules. The parameter lambda of an equal-quantile rule is the maximal probability of satiation imposed on agents - for each agent, the prob-ability that his assignment is no less than his realized need is at most lambda. It determines the extent to which the resource should be used to satiate agents. If the resource is no more than the sum of the agents' lambda-quantile assignments, it is fully allocated and the rule equalizes the probabilities of satiation across agents. Otherwise, each agent just receives his lambda-quantile assignment. The equal-quantile class is characterized by four axioms, conditional strict ranking, continuity, double consistency, and coordinality. All are variants of familiar properties in the literature on deterministic fair division problems. Moreover, the rules are optimal with respect to two utilitarian objectives. The optimality results not only provide welfare interpretations of lambda, but also show how the rules balance the concerns for generating waste and deficit across agents. (c) 2021 Elsevier Inc. All rights reserved.