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Order Symmetry: A New Fairness Criterion for Assignment Mechanisms

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  • Freeman, Rupert
  • Pritchard, Geoffrey
  • Wilson, Mark

Abstract

We introduce a new fairness criterion, order symmetry, for assignment mechanisms that match n objects to n agents with ordinal preferences over the objects. An assignment mechanism is order symmetric with respect to some probability measure over preference profiles if every agent is equally likely to receive their favorite object, every agent is equally likely to receive their second favorite, and so on. When associated with a sufficiently symmetric probability measure, order symmetry is a relaxation of anonymity that, crucially, can be satisfied by discrete assignment mechanisms. Furthermore, it can be achieved without sacrificing other desirable axiomatic properties satisfied by existing mechanisms. In particular, we show that it can be achieved in conjunction with strategyproofness and ex post efficiency via the top trading cycles mechanism (but not serial dictatorship). We additionally design a novel mechanism that is both order symmetric and ordinally efficient. The practical utility of order symmetry is substantiated by simulations on Impartial Culture and Mallows-distributed preferences for four common assignment mechanisms.

Suggested Citation

  • Freeman, Rupert & Pritchard, Geoffrey & Wilson, Mark, 2021. "Order Symmetry: A New Fairness Criterion for Assignment Mechanisms," SocArXiv xt37c, Center for Open Science.
  • Handle: RePEc:osf:socarx:xt37c
    DOI: 10.31219/osf.io/xt37c
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    References listed on IDEAS

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    1. Bogomolnaia, Anna & Moulin, Herve, 2001. "A New Solution to the Random Assignment Problem," Journal of Economic Theory, Elsevier, vol. 100(2), pages 295-328, October.
    2. Mohammad Akbarpour & Afshin Nikzad, 2020. "Approximate Random Allocation Mechanisms," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 87(6), pages 2473-2510.
    3. William Thomson, 2007. "Children Crying at Birthday Parties. Why?," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 31(3), pages 501-521, June.
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    5. Nesterov, Alexander S., 2017. "Fairness and efficiency in strategy-proof object allocation mechanisms," Journal of Economic Theory, Elsevier, vol. 170(C), pages 145-168.
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    Cited by:

    1. Geoffrey Pritchard & Mark C. Wilson, 2022. "Asymptotic welfare performance of Boston assignment algorithms," Papers 2205.15418, arXiv.org.
    2. Xinghua Long & Rodrigo A. Velez, 2021. "Balanced House Allocation," Papers 2109.01992, arXiv.org.

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