Stability and Efficiency of Random Serial Dictatorship

TL;DR

This paper proves that the cutoffs in Random Serial Dictatorship converge in large environments with many students and schools, using advanced probabilistic tools to handle arbitrary preferences.

Contribution

It introduces a novel analytic approach to establish non-asymptotic convergence of RSD cutoffs in complex environments, extending prior work with new probabilistic techniques.

Findings

Convergence of RSD cutoffs when m ln m << n

Sharpness of the convergence result demonstrated

Concentration of RSD probabilities under arbitrary preferences

Abstract

This paper establishes non-asymptotic convergence of the cutoffs in Random serial dictatorship in an environment with many students, many schools, and arbitrary student preferences. Convergence is shown to hold when the number of schools, $m$, and the number of students, $n$, satisfy the relation $m \ln m \ll n$, and we provide an example showing that this result is sharp. We differ significantly from prior work in the mechanism design literature in our use of analytic tools from randomized algorithms and discrete probability, which allow us to show concentration of the RSD lottery probabilities and cutoffs even against adversarial student preferences.