Ordinal Bayesian incentive compatibility in random assignment model

We explore the consequences of weakening notion incentive compatibility from strategy-proofness to ordinal Bayesian (OBIC) in random assignment model. If common prior agents is a uniform prior, then large class mechanisms are OBIC with respect this -- includes probabilistic serial mechanism. introduce robust version OBIC: mechanism locally if it all independent priors some neighborhood given prior. show that every satisfying mild property called elementary monotonicity strategy-proof. This leads strengthening impossibility result Bogomolnaia and Moulin (2001): there at least four agents, no ordinally efficient equal treatment equals.