Using lotteries is a common tool for allocating indivisible goods. Since obtaining preferences
over lotteries is often difficult, real-life mechanisms usually rely on ordinal preferences over
deterministic outcomes. Bogomolnaia and Moulin (J. Econom. Theory 19 (2002) 623) show
that the outcome of an ex post efficient mechanism may be stochastically dominated. They
define a random assignment to be ordinally efficient if and only if it is not stochastically
dominated. In this paper we investigate the relation between ex post efficiency and ordinal …