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The fractional Boston random assignment rule and its axiomatic characterization

Author

Listed:
  • Yajing Chen

    (East China University of Science and Technology)

  • Patrick Harless

    (University of Arizona)

  • Zhenhua Jiao

    (Shanghai University of International Business and Economics)

Abstract

This study considers the problem of random assignment of a set of objects to a set of agents based on strict ordinal preferences of the agents. We analyze the fractional Boston rule, which is a generalization of the classical Boston rule to random assignment environments. We introduce two new axioms—stochastic dominance (sd)-rank-efficiency and equal-rank envy-freeness—which are respectively efficiency and fairness conditions that respect preference ranks. Sd-rank-efficiency implies ordinal efficiency, which is an efficiency concept defined by Bogomolnaia and Moulin (J Econ Theory 100(2):295–328, 2001) for random assignment environments in the sense of first-order stochastic dominance. Equal-rank envy-freeness implies equal treatment of equals. Sd-rank-efficiency and equal-rank envy-freeness characterize the fractional Boston rule.

Suggested Citation

  • Yajing Chen & Patrick Harless & Zhenhua Jiao, 2024. "The fractional Boston random assignment rule and its axiomatic characterization," Review of Economic Design, Springer;Society for Economic Design, vol. 28(1), pages 21-43, February.
    • Handle: RePEc:spr:reecde:v:28:y:2024:i:1:d:10.1007_s10058-023-00329-7
    DOI: 10.1007/s10058-023-00329-7
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    Keywords

    Random assignment; Fractional Boston rule; Sd-rank-efficiency; Equal-rank envy-freeness; Axiomatic characterization;
    All these keywords.

    JEL classification:

    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
    • 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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