Probabilistic assignment of objects: Characterizing the serial rule

We study the problem of assigning a set of objects to a set of agents, when each agent receives one object and has strict preferences over the objects. In the absence of monetary transfers, we focus on the probabilistic rules, which take the ordinal preferences as input. We characterize the serial rule, proposed by Bogomolnaia and Moulin (2001) [2]: it is the only rule satisfying sd efficiency, sd no-envy, and bounded invariance. A special representation of feasible assignment matrices by means of consumption processes is the key to the simple and intuitive proof of our main result.