Efficient Rules for Probabilistic Assignment

Abstract

We propose an algorithm to construct sd-efficient probabilistic allocations of objects. Our algorithm proceeds in discrete rounds and distributes probability shares of objects sequentially yielding two natural degrees of freedom: selection rules governing the choice of objects in each round and distribution rules governing the dispensation of probability shares. The transparent procedure tightly connects properties of the rule to these choices making it ideally suited for practical applications. First proving that the algorithm identifies all sd-efficient allocations, we apply the technique to obtain a surprising and “decentralized” representation of the serial rule. Further applications construct new sd-efficient rules.