A Comment on the Averseness of Random Serial Dictatorship to Stochastic Dominance Efficiency

Random Serial Dictatorship (RSD) is arguably the most well-known and widely used assignment rule. Although it returns an ex post efficient assignment, Bogomolnaia and Moulin (A new solution to the random assignment problem, J. Econ. Theory 100, 295–328) proved that RSD may not be SD-efficient (efficient with respect stochastic dominance). The result raises the following question: under what conditions is RSD not SD-efficient? We characterize the conditions under which the RSD assignment is not SD-efficient: the RSD assignment is not SD-efficient if and only if an ex post assignment exists that is not SD-efficient. Hence RSD can be viewed as being inherently averse to SD-efficiency.