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Fairness and efficiency in a random assignment: Three impossibility results

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  • Nesterov, Alexander S.

Abstract

This paper considers the problem of allocating N indivisible objects among N agents according to their preferences when transfers are not allowed, and studies the tradeoff between fairness and efficiency in the class of strategy-proof mechanisms. The main finding is that for strategy-proof mechanisms the following efficiency and fairness criteria are mutually incompatible: (1) Ex-post efficiency and envy-freeness, (2) ordinal efficiency and weak envy-freeness and (3) ordinal efficiency and equal division lower bound. Result (1) is the first impossibility result for this setting that uses ex-post efficiency; results (2) and (3) are more relevant for practical implementation than similar results in the literature. In addition, for N = 3 the paper strengthens the characterization result by Bogomolnaia and Moulin (2001): the random serial dictatorship mechanism is the unique strategy-proof, ex-post efficient mechanism that eliminates strict envy between agents with the same preferences.

Suggested Citation

  • Nesterov, Alexander S., 2014. "Fairness and efficiency in a random assignment: Three impossibility results," Discussion Papers, Research Unit: Market Behavior SP II 2014-211, WZB Berlin Social Science Center.
    • Handle: RePEc:zbw:wzbmbh:spii2014211
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    Cited by:

    1. Onur Kesten & Morimitsu Kurino & Alexander S. Nesterov, 2017. "Efficient lottery design," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 48(1), pages 31-57, January.
    2. Bade, Sophie, 2016. "Fairness and group-strategyproofness clash in assignment problems," Journal of Economic Theory, Elsevier, vol. 165(C), pages 257-262.

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    More about this item

    Keywords

    random assignment; random serial dictatorship; strategy-proofness; ex-post efficiency; weak envy-freeness; equal division lower bound;
    All these keywords.

    JEL classification:

    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
    • D78 - Microeconomics - - Analysis of Collective Decision-Making - - - Positive Analysis of Policy Formulation and Implementation

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