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Fair solutions to the random assignment problem

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  • Basteck, Christian

Abstract

We study the problem of assigning indivisible goods to individuals where each is to receive one good. To guarantee fairness in the absence of monetary compensation, we consider random assignments that individuals evaluate according to first order stochastic dominance (sd). In particular, we find that solutions which guarantee sd-no-envy (e.g. the Probabilistic Serial) are incompatible even with the weak sd-core from equal division. Solutions on the other hand that produce assignments in the strong sd-core from equal division (e.g. Hylland and Zeckhauser’s Walrasian Equilibria from Equal Incomes) are incompatible with the strong sd-equal-division-lower-bound. As an alternative, we present a solution, based on Walrasian equilibria, that is sd-efficient, in the weak sd-core from equal division, and satisfies the strong sd-equal-division-lower-bound.

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  • Basteck, Christian, 2018. "Fair solutions to the random assignment problem," Journal of Mathematical Economics, Elsevier, vol. 79(C), pages 163-172.
    • Handle: RePEc:eee:mateco:v:79:y:2018:i:c:p:163-172
    DOI: 10.1016/j.jmateco.2018.02.006
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    1. Stergios Athanassoglou & Jay Sethuraman, 2011. "House allocation with fractional endowments," International Journal of Game Theory, Springer;Game Theory Society, vol. 40(3), pages 481-513, August.
    2. Yinghua He & Antonio Miralles & Marek Pycia & Jianye Yan, 2018. "A Pseudo-Market Approach to Allocation with Priorities," American Economic Journal: Microeconomics, American Economic Association, vol. 10(3), pages 272-314, August.
    3. Atila Abdulkadiro?lu & Yeon-Koo Che & Yosuke Yasuda, 2015. "Expanding "Choice" in School Choice," American Economic Journal: Microeconomics, American Economic Association, vol. 7(1), pages 1-42, February.
    4. Thomson, William, 2011. "Chapter Twenty-One - Fair Allocation Rules," Handbook of Social Choice and Welfare, in: K. J. Arrow & A. K. Sen & K. Suzumura (ed.), Handbook of Social Choice and Welfare, edition 1, volume 2, chapter 21, pages 393-506, Elsevier.
    5. 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.
    6. Manea, Mihai, 2008. "A constructive proof of the ordinal efficiency welfare theorem," Journal of Economic Theory, Elsevier, vol. 141(1), pages 276-281, July.
    7. Andreu Mas-Colell, 1992. "Equilibrium Theory with Possibly Satiated Preferences," Palgrave Macmillan Books, in: Mukul Majumdar (ed.), Equilibrium and Dynamics, chapter 9, pages 201-213, Palgrave Macmillan.
    8. 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.
    9. Onur Kesten & Morimitsu Kurino & Alexander S. Nesterov, 2017. "Efficient lottery design," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 48(1), pages 31-57, January.
    10. Pathak, Parag A. & Shi, Peng, 2021. "How well do structural demand models work? Counterfactual predictions in school choice," Journal of Econometrics, Elsevier, vol. 222(1), pages 161-195.
    11. Aytek Erdil & Haluk Ergin, 2008. "What's the Matter with Tie-Breaking? Improving Efficiency in School Choice," American Economic Review, American Economic Association, vol. 98(3), pages 669-689, June.
    12. , A. & ,, 2011. "Lotteries in student assignment: An equivalence result," Theoretical Economics, Econometric Society, vol. 6(1), January.
    13. 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.
    14. Eric Budish, 2011. "The Combinatorial Assignment Problem: Approximate Competitive Equilibrium from Equal Incomes," Journal of Political Economy, University of Chicago Press, vol. 119(6), pages 1061-1103.
    15. McLennan, Andrew, 2002. "Ordinal Efficiency and the Polyhedral Separating Hyperplane Theorem," Journal of Economic Theory, Elsevier, vol. 105(2), pages 435-449, August.
    16. Heo, Eun Jeong, 2014. "Probabilistic assignment problem with multi-unit demands: A generalization of the serial rule and its characterization," Journal of Mathematical Economics, Elsevier, vol. 54(C), pages 40-47.
    17. Basteck, Christian, 2018. "Fair solutions to the random assignment problem," Journal of Mathematical Economics, Elsevier, vol. 79(C), pages 163-172.
    18. Haris Aziz & Yoichi Kasajima, 2017. "Impossibilities for probabilistic assignment," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 49(2), pages 255-275, August.
    19. Nesterov, Alexander S., 2017. "Fairness and efficiency in strategy-proof object allocation mechanisms," Journal of Economic Theory, Elsevier, vol. 170(C), pages 145-168.
    20. 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.
    21. Kesten, Onur, 2009. "Why do popular mechanisms lack efficiency in random environments?," Journal of Economic Theory, Elsevier, vol. 144(5), pages 2209-2226, September.
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    Cited by:

    1. Basteck, Christian & Ehlers, Lars, 2023. "Strategy-proof and envy-free random assignment," Journal of Economic Theory, Elsevier, vol. 209(C).
    2. Basteck, Christian, 2018. "Fair solutions to the random assignment problem," Journal of Mathematical Economics, Elsevier, vol. 79(C), pages 163-172.
    3. Basteck, Christian & Ehlers, Lars H., 2022. "Strategy-proof and envy-free random assignment," Discussion Papers, Research Unit: Market Behavior SP II 2022-208, WZB Berlin Social Science Center.
    4. Rasoul Ramezanian & Mehdi Feizi, 2021. "Ex-post favoring ranks: a fairness notion for the random assignment problem," Review of Economic Design, Springer;Society for Economic Design, vol. 25(3), pages 157-176, September.
    5. Basteck, Christian & Ehlers, Lars, 2021. "Strategy-Proof and Envy-Free Random Assignment," Rationality and Competition Discussion Paper Series 307, CRC TRR 190 Rationality and Competition.
    6. Shende, Priyanka & Purohit, Manish, 2023. "Strategy-proof and envy-free mechanisms for house allocation," Journal of Economic Theory, Elsevier, vol. 213(C).
    7. Jingsheng Yu & Jun Zhang, 2020. "Efficient and fair trading algorithms in market design environments," Papers 2005.06878, arXiv.org, revised May 2021.

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