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

TL;DR

This paper examines the conditions under which Random Serial Dictatorship (RSD) fails to be stochastic dominance efficient, showing that RSD's inefficiency is linked to the existence of non-SD-efficient ex post assignments, highlighting its inherent aversion to SD-efficiency.

Contribution

It provides a detailed characterization of when RSD is not SD-efficient, connecting RSD's inefficiency to the existence of non-SD-efficient ex post assignments.

Findings

RSD is not SD-efficient if and only if a non-SD-efficient ex post assignment exists.

RSD inherently tends to be averse to SD-efficiency.

The characterization aligns with Manea's 2009 results.

Abstract

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).