An axiomatization of the random priority rule

We study the problem of assigning indivisible objects to agents where each is to receive at most one. To ensure fairness in the absence of monetary transfers, we consider random assignments. Random Priority, also known as Random Serial Dictatorship, is characterized by equal-treatment-of-equals, ex-post efficiency and probabilistic monotonicity - whenever preferences change so that a given deterministic assignment is ranked higher by all agents, the probability of that assignment arising should not decrease. Probabilistic monotonicity implies strategy-proofness for random assignment problems and is equivalent to it on the universal domain of strict preferences; for deterministic rules it coincides with Maskin-monotonicity.