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Fair Division in the Internet Age

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  • Hervé Moulin

Abstract

Fair division, a key concern in the design of many social institutions, has for 70 years been the subject of interdisciplinary research at the interface of mathematics, economics, and game theory. Motivated by the proliferation of moneyless transactions on the internet, the computer science community has recently taken a deep interest in fairness principles and practical division rules. The resulting literature brings a fresh concern for computational simplicity (scalable rules) and realistic implementation. In this review of the most salient fair division results of the past 30 years, I concentrate on division rules with the best potential for practical implementation. The critical design parameter is the message space that the agents must use to report their individual preferences. A simple preference domain is key both to realistic implementation and to the existence of division rules with strong normative and incentive properties. I discuss successively the one-dimensional single-peaked domain, Leontief utilities, ordinal ranking, dichotomous preferences, and additive utilities. Some of the theoretical results in the latter domain are already implemented in the user-friendly SPLIDDIT platform (http://spliddit.org).

Suggested Citation

  • Hervé Moulin, 2019. "Fair Division in the Internet Age," Annual Review of Economics, Annual Reviews, vol. 11(1), pages 407-441, August.
    • Handle: RePEc:anr:reveco:v:11:y:2019:p:407-441
    DOI: 10.1146/annurev-economics-080218-025559
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    Citations

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    Cited by:

    1. Anna Bogomolnaia & Hervé Moulin & Fedor Sandomirskiy, 2022. "On the Fair Division of a Random Object," Management Science, INFORMS, vol. 68(2), pages 1174-1194, February.
    2. Anna Bogomolnaia & Hervé Moulin, 2023. "Guarantees in Fair Division: General or Monotone Preferences," Mathematics of Operations Research, INFORMS, vol. 48(1), pages 160-176, February.
    3. Fedor Sandomirskiy & Philip Ushchev, 2024. "The geometry of consumer preference aggregation," Papers 2405.06108, arXiv.org.
    4. Pasin Manurangsi & Warut Suksompong, 2020. "Closing Gaps in Asymptotic Fair Division," Papers 2004.05563, arXiv.org.
    5. Haris Aziz & Xinhang Lu & Mashbat Suzuki & Jeremy Vollen & Toby Walsh, 2023. "Best-of-Both-Worlds Fairness in Committee Voting," Papers 2303.03642, arXiv.org, revised Dec 2023.
    6. Hadi Hosseini, 2023. "The Fairness Fair: Bringing Human Perception into Collective Decision-Making," Papers 2312.14402, arXiv.org.
    7. Shende, Priyanka & Purohit, Manish, 2023. "Strategy-proof and envy-free mechanisms for house allocation," Journal of Economic Theory, Elsevier, vol. 213(C).
    8. Hadi Hosseini & Zhiyi Huang & Ayumi Igarashi & Nisarg Shah, 2022. "Class Fairness in Online Matching," Papers 2203.03751, arXiv.org.
    9. Hougaard, Jens Leth & Tvede, Mich, 2022. "Trouble comes in threes: Core stability in minimum cost connection networks," European Journal of Operational Research, Elsevier, vol. 297(1), pages 319-324.
    10. Gersbach, Hans & Tejada, Oriol, 2020. "Semi-flexible Majority Rules for Public Good Provision," CEPR Discussion Papers 15099, C.E.P.R. Discussion Papers.
    11. Anna Bogomolnaia & Herve Moulin, 2022. "Fair Division with Money and Prices," Papers 2202.08117, arXiv.org.
    12. Di Feng & Jacob Coreno, 2024. "Justified Fairness in House Allocation Problems: two Characterizations of Strategy-proof Mechanisms," Papers 2407.14101, arXiv.org.
    13. Caspari, Gian, 2020. "Booster draft mechanism for multi-object assignment," ZEW Discussion Papers 20-074, ZEW - Leibniz Centre for European Economic Research.
    14. Anna Bogomolnaia & Herv'e Moulin, 2024. "Guaranteed shares of benefits and costs," Papers 2406.14198, arXiv.org, revised Nov 2024.
    15. Priyanka Shende & Manish Purohit, 2020. "Strategy-proof and Envy-free Mechanisms for House Allocation," Papers 2010.16384, arXiv.org.
    16. Gerrit Bauch & Frank Riedel, 2022. "The Texas Shootout under Uncertainty," Papers 2211.10089, arXiv.org.
    17. Mithun Chakraborty & Ayumi Igarashi & Warut Suksompong & Yair Zick, 2019. "Weighted Envy-Freeness in Indivisible Item Allocation," Papers 1909.10502, arXiv.org, revised Mar 2021.
    18. Jens Leth Hougaard & Mich Tvede, 2020. "Trouble Comes in Threes: Core stability in Minimum Cost Connection Networks," IFRO Working Paper 2020/07, University of Copenhagen, Department of Food and Resource Economics.
    19. Sheung Man Yuen & Warut Suksompong, 2023. "Extending the Characterization of Maximum Nash Welfare," Papers 2301.03798, arXiv.org, revised Feb 2023.
    20. Dall’Aglio, Marco, 2023. "Fair division of goods in the shadow of market values," European Journal of Operational Research, Elsevier, vol. 307(2), pages 785-801.
    21. Yuen, Sheung Man & Suksompong, Warut, 2023. "Extending the characterization of maximum Nash welfare," Economics Letters, Elsevier, vol. 224(C).
    22. Kondratev, Aleksei Y. & Nesterov, Alexander S., 2022. "Minimal envy and popular matchings," European Journal of Operational Research, Elsevier, vol. 296(3), pages 776-787.
    23. Vijay V. Vazirani, 2024. "Equitable Core Imputations via a New Adaptation of The Primal-Dual Framework," Papers 2402.11437, arXiv.org, revised Dec 2024.
    24. Cornilly, Dries & Puccetti, Giovanni & Rüschendorf, Ludger & Vanduffel, Steven, 2022. "Fair allocation of indivisible goods with minimum inequality or minimum envy," European Journal of Operational Research, Elsevier, vol. 297(2), pages 741-752.

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