A new solution to the random assignment problem

A random assignment is ordinally efficient if it is not stochastically domi nated with respect to individual preferences over sure objects. Ordinal eff iciency implies (is implied by) ex post (ex ante) efficiency. A simple algo rithm characterizes ordinally efficient assignments: our solution, probabil istic serial (PS), is a central element within their set. Random priority ( RP) orders agents from the uniform distribution, then lets them choose succ essively their best remaining object. RP is ex post, but not always ordinal ly, efficient. PS is envy-free, RP is not; RP is strategy-proof, PS is not. Ordinal efficiency, Strategyproofness, and equal treatment of equals are i ncompatible. (C) 2001 Academic Press.