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Upper-contour strategy-proofness in the probabilistic assignment problem

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  • Youngsub Chun

    (Seoul National University)

  • Kiyong Yun

    (Seoul National University)

Abstract

Bogomolnaia and Moulin (J Econ Theory 100:295–328, 2001) show that there is no rule satisfying stochastic dominance efficiency,equal treatment of equals and stochastic dominance strategy-proofness for a probabilistic assignment problem of indivisible objects. Recently, Mennle and Seuken (Partial strategyproofness: relaxing strategy-proofness for the random assignment problem. Mimeo, 2017) show that stochastic dominance strategy-proofness is equivalent to the combination of three axioms, swap monotonicity,upper invariance, and lower invariance. In this paper, we introduce a weakening of stochastic dominance strategy-proofness, called upper-contour strategy-proofness, which requires that if the upper-contour sets of some objects are the same in two preference relations, then the sum of probabilities assigned to the objects in the two upper-contour sets should be the same. First, we show that upper-contour strategy-proofness is equivalent to the combination of two axioms, upper invariance and lower invariance. Next, we show that the impossibility result still holds even though stochastic dominance strategy-proofness is weakened to upper-contour strategy-proofness.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:sochwe:v:54:y:2020:i:4:d:10.1007_s00355-019-01226-1
    DOI: 10.1007/s00355-019-01226-1
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    References listed on IDEAS

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    Cited by:

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    2. Feizi, Mehdi & Ramezanian, Rasoul, 2023. "A new impossibility result for random assignments," Journal of Mathematical Economics, Elsevier, vol. 107(C).
    3. 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.
    4. Hirata, Daisuke & 平田, 大祐 & Kasuya, Yusuke & 糟谷, 祐介 & Okumura, Yasunori & 奥村, 保規, 2023. "Stability, Strategy-Proofness, and Respect for Improvements," Discussion Papers 2023-01, Graduate School of Economics, Hitotsubashi University.
    5. Roy, Souvik & Sadhukhan, Soumyarup, 2022. "On the equivalence of strategy-proofness and upper contour strategy-proofness for randomized social choice functions," Journal of Mathematical Economics, Elsevier, vol. 99(C).

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