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Impossibility results in the probabilistic assignment problem with stochastic same-sidedness and minimal invariance

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  • Yun, Kiyong

Abstract

Bogomolnaia and Moulin (2001) demonstrate the impossibility of designing a rule that simultaneously satisfies stochastic dominance efficiency, equal treatment of equals, and stochastic dominance strategy-proofness in the context of the probabilistic assignment problem with indivisible objects. Despite attempts to relax these conditions by introducing concepts like upper contour strategy-proofness or robust ex-post efficiency, the impossibility results remain. Recently, Bandhu et al. (2024) introduced the concept of stochastic same-sidedness in the random voting model. This condition stipulates that if an agent modifies their preference by swapping two consecutively ranked objects, then (1) the sum of probabilities assigned to objects strictly higher than the swapped pair should remain unchanged, and (2) the sum of probabilities assigned to the swapped pair should also remain constant. We first show that the impossibility persists even when stochastic dominance strategy-proofness is weakened to stochastic same-sidedness. We then decompose stochastic same-sidedness into three minimal invariance axioms and use these to establish further impossibility results.

Suggested Citation

  • Yun, Kiyong, 2025. "Impossibility results in the probabilistic assignment problem with stochastic same-sidedness and minimal invariance," Journal of Mathematical Economics, Elsevier, vol. 121(C).
    • Handle: RePEc:eee:mateco:v:121:y:2025:i:c:s0304406825001004
    DOI: 10.1016/j.jmateco.2025.103183
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    References listed on IDEAS

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    1. Liu, Peng, 2020. "Random assignments on sequentially dichotomous domains," Games and Economic Behavior, Elsevier, vol. 121(C), pages 565-584.
    2. Muto, Nozomu & Sato, Shin, 2017. "An impossibility under bounded response of social choice functions," Games and Economic Behavior, Elsevier, vol. 106(C), pages 1-15.
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    10. Feizi, Mehdi & Ramezanian, Rasoul, 2023. "A new impossibility result for random assignments," Journal of Mathematical Economics, Elsevier, vol. 107(C).
    11. Youngsub Chun & Kiyong Yun, 2020. "Upper-contour strategy-proofness in the probabilistic assignment problem," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 54(4), pages 667-687, April.
    12. Sarvesh Bandhu & Abhinaba Lahiri & Anup Pramanik, 2024. "Stochastic same-sidedness in the random voting model," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 62(1), pages 167-196, February.
    13. Yoichi Kasajima, 2013. "Probabilistic assignment of indivisible goods with single-peaked preferences," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 41(1), pages 203-215, June.
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    16. Ramezanian, Rasoul & Feizi, Mehdi, 2022. "Robust ex-post Pareto efficiency and fairness in random assignments: Two impossibility results," Games and Economic Behavior, Elsevier, vol. 135(C), pages 356-367.
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    Cited by:

    1. Yun, Kiyong & Chun, Youngsub, 2026. "A maximal domain for weak stochastic dominance strategy-proofness of the extended probabilistic serial correspondence," Games and Economic Behavior, Elsevier, vol. 155(C), pages 10-26.

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    JEL classification:

    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • D61 - Microeconomics - - Welfare Economics - - - Allocative Efficiency; Cost-Benefit Analysis
    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement

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