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 is supposed to receive only one object and has strict preferences over the objects. In the absence of monetary transfers, we focus on the probabilistic rules, which takes the ordinal preferences as input (the ordering over objects by each agent is submitted, but the relative cardinal intensities of their preferences are not). We present a characterization of the serial rule proposed by Bogomolnaia and Moulin (2001) in this model. The serial rule is the only rule satisfying sd efficiency, sd no-envy, and bounded invariance (where "sd" stands for "stochastic dominance"). A special representation of feasible assignments via consumption processes over time is the key to the simple and intuitive proof of our main result. This technique also allows us to present a simple unifying argument for a number of related earlier and concurrent results