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Stability and Efficiency of Random Serial Dictatorship

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  • Suhas Vijaykumar

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.

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  • Suhas Vijaykumar, 2021. "Stability and Efficiency of Random Serial Dictatorship," Papers 2110.07024, arXiv.org.
    • Handle: RePEc:arx:papers:2110.07024
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    References listed on IDEAS

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    1. Konrad Menzel, 2015. "Large Matching Markets as Two‐Sided Demand Systems," Econometrica, Econometric Society, vol. 83(3), pages 897-941, May.
    2. Atila Abdulkadroǧlu & Joshua D. Angrist & Yusuke Narita & Parag A. Pathak & Roman A. Zarate, 2017. "Regression Discontinuity in Serial Dictatorship: Achievement Effects at Chicago's Exam Schools," American Economic Review, American Economic Association, vol. 107(5), pages 240-245, May.
    3. Eduardo M. Azevedo & Jacob D. Leshno, 2016. "A Supply and Demand Framework for Two-Sided Matching Markets," Journal of Political Economy, University of Chicago Press, vol. 124(5), pages 1235-1268.
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