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A theory of fair random allocation under priorities

Author

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  • Han, Xiang

    (School of Economics, Shanghai University of Finance and Economics)

Abstract

In the allocation of indivisible objects under weak priorities, a common practice is to break the ties using a lottery and randomize over deterministic mechanisms. Such randomizations usually lead to unfairness and inefficiency ex-ante. We propose and study the concept of ex-ante fairness for random allocations, extending some key results in the one-sided and two-sided matching markets. It is shown that the set of ex-ante fair random allocations forms a complete and distributive lattice under first-order stochastic dominance relations, and the agent-optimal ex-ante fair mechanism includes both the deferred acceptance algorithm and the probabilistic serial mechanism as special cases. Instead of randomizing over deterministic mechanisms, our mechanism is constructed using the division method, a new general way of constructing random mechanisms from deterministic mechanisms. As additional applications, we demonstrate that several previous extensions of the probabilistic serial mechanism have their foundations in existing deterministic mechanisms.

Suggested Citation

  • Han, Xiang, 2024. "A theory of fair random allocation under priorities," Theoretical Economics, Econometric Society, vol. 19(3), July.
    • Handle: RePEc:the:publsh:5262
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    More about this item

    Keywords

    Indivisible object; weak priority; random allocation; fairness; deferred acceptance algorithm; probabilistic serial mechanism;
    All these keywords.

    JEL classification:

    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • D47 - Microeconomics - - Market Structure, Pricing, and Design - - - Market Design
    • 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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