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? In this comment, we give a detailed argument that 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. The characterization was proved by Manea (2009).