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 resolves. We propose a parametric class of division rules we call equal-quantile rules. The parameter λ of an equal-quantile rule is the maximal probability of satiation imposed on agents — for each agent, the probability that his assignment is no less than his realized need is at most λ. 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' λ-quantile assignments, it is fully allocated and the rule equalizes the probabilities of satiation across agents. Otherwise, each agent just receives his λ-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 λ, but also show how the rules balance the concerns for generating waste and deficit across agents.