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Probabilistic assignment of indivisible objects when agents have the same preferences except the ordinal ranking of one object

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  • Chang, Hee-In
  • Chun, Youngsub

Abstract

Bogomolnaia and Moulin (2001) show that there is no rule satisfying equal treatment of equals, stochastic dominance efficiency, and stochastic dominance strategyproofness for a probabilistic assignment problem of indivisible objects. Kasajima (2013) shows that the incompatibility result still holds when agents are restricted to have single-peaked preferences. In this paper, we further restrict the domain and investigate the existence of rules satisfying the three properties. As it turns out, the three properties are still incompatible even if all agents have the same preferences except the ordinal ranking of one object.

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  • Chang, Hee-In & Chun, Youngsub, 2017. "Probabilistic assignment of indivisible objects when agents have the same preferences except the ordinal ranking of one object," Mathematical Social Sciences, Elsevier, vol. 90(C), pages 80-92.
    • Handle: RePEc:eee:matsoc:v:90:y:2017:i:c:p:80-92
    DOI: 10.1016/j.mathsocsci.2017.08.001
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    References listed on IDEAS

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    1. Bogomolnaia, Anna, 2015. "Random assignment: Redefining the serial rule," Journal of Economic Theory, Elsevier, vol. 158(PA), pages 308-318.
    2. Atila Abdulkadiroglu & Tayfun Sonmez, 1998. "Random Serial Dictatorship and the Core from Random Endowments in House Allocation Problems," Econometrica, Econometric Society, vol. 66(3), pages 689-702, May.
    3. Bogomolnaia, Anna & Heo, Eun Jeong, 2012. "Probabilistic assignment of objects: Characterizing the serial rule," Journal of Economic Theory, Elsevier, vol. 147(5), pages 2072-2082.
    4. Bogomolnaia, Anna & Moulin, Herve, 2015. "Size versus fairness in the assignment problem," Games and Economic Behavior, Elsevier, vol. 90(C), pages 119-127.
    5. Kojima, Fuhito, 2009. "Random assignment of multiple indivisible objects," Mathematical Social Sciences, Elsevier, vol. 57(1), pages 134-142, January.
    6. Bogomolnaia, Anna & Moulin, Herve, 2001. "A New Solution to the Random Assignment Problem," Journal of Economic Theory, Elsevier, vol. 100(2), pages 295-328, October.
    7. Anna Bogomolnaia & Herve Moulin, 2004. "Random Matching Under Dichotomous Preferences," Econometrica, Econometric Society, vol. 72(1), pages 257-279, January.
    8. Hashimoto, Tadashi & Hirata, Daisuke & Kesten, Onur & Kurino, Morimitsu & Unver, Utku, 2014. "Two axiomatic approaches to the probabilistic serial mechanism," Theoretical Economics, Econometric Society, vol. 9(1), January.
    9. Abdulkadiroglu, Atila & Sonmez, Tayfun, 2003. "Ordinal efficiency and dominated sets of assignments," Journal of Economic Theory, Elsevier, vol. 112(1), pages 157-172, September.
    10. Yeon-Koo Che & Fuhito Kojima, 2010. "Asymptotic Equivalence of Probabilistic Serial and Random Priority Mechanisms," Econometrica, Econometric Society, vol. 78(5), pages 1625-1672, September.
    11. Erdil, Aytek, 2014. "Strategy-proof stochastic assignment," Journal of Economic Theory, Elsevier, vol. 151(C), pages 146-162.
    12. Katta, Akshay-Kumar & Sethuraman, Jay, 2006. "A solution to the random assignment problem on the full preference domain," Journal of Economic Theory, Elsevier, vol. 131(1), pages 231-250, November.
    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.
    14. Hylland, Aanund & Zeckhauser, Richard, 1979. "The Efficient Allocation of Individuals to Positions," Journal of Political Economy, University of Chicago Press, vol. 87(2), pages 293-314, April.
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    Cited by:

    1. Liu, Peng, 2020. "Random assignments on sequentially dichotomous domains," Games and Economic Behavior, Elsevier, vol. 121(C), pages 565-584.
    2. Felix Brandt & Matthias Greger & Ren'e Romen, 2023. "Towards a Characterization of Random Serial Dictatorship," Papers 2303.11976, arXiv.org, revised Jun 2023.
    3. Balbuzanov, Ivan, 2020. "Short trading cycles: Paired kidney exchange with strict ordinal preferences," Mathematical Social Sciences, Elsevier, vol. 104(C), pages 78-87.
    4. Liu, Peng & Zeng, Huaxia, 2019. "Random assignments on preference domains with a tier structure," Journal of Mathematical Economics, Elsevier, vol. 84(C), pages 176-194.
    5. Brandt, Felix & Saile, Christian & Stricker, Christian, 2022. "Strategyproof social choice when preferences and outcomes may contain ties," Journal of Economic Theory, Elsevier, vol. 202(C).
    6. Aziz, Haris & Brandl, Florian & Brandt, Felix & Brill, Markus, 2018. "On the tradeoff between efficiency and strategyproofness," Games and Economic Behavior, Elsevier, vol. 110(C), pages 1-18.
    7. Basteck, Christian & Ehlers, Lars, 2023. "Strategy-proof and envy-free random assignment," Journal of Economic Theory, Elsevier, vol. 209(C).
    8. 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.
    9. Alva, Samson & Manjunath, Vikram, 2020. "The impossibility of strategy-proof, Pareto efficient, and individually rational rules for fractional matching," Games and Economic Behavior, Elsevier, vol. 119(C), pages 15-29.
    10. Chatterji, Shurojit & Liu, Peng, 2020. "Random assignments of bundles," Journal of Mathematical Economics, Elsevier, vol. 87(C), pages 15-30.

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