An axiomatization of the random priority rule

We study the problem of assigning indivisible objects to agents where each is to receive one object. To ensure fairness in the absence of monetary compensation, we consider random assignments. Random Priority, also known as Random Serial Dictatorship, is characterized by symmetry, ex-post efficiency, and probabilistic (Maskin) monotonicity - whenever preferences change so that a given deterministic assignment is ranked weakly higher by all agents, the probability of that assignment being chosen should be weakly larger. Probabilistic monotonicity implies strategy-proofness for random assignment problems and is equivalent on a general social choice domain; for deterministic rules it coincides with Maskin monotonicity.