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Fair Division Of Indivisible Items

Author

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  • Steven J. Brams
  • Paul H. Edelman
  • Peter C. Fishburn

Abstract

This paper analyzes criteria of fair division of a set of indivisible items among people whose revealed preferences are limited to rankings of the items and for whom no side payments are allowed. The criteria include refinements of Pareto optimality and envy-freeness as well as dominance-freeness, evenness of shares, and two criteria based on equally-spaced surrogate utilities, referred to as maxsum and equimax. Maxsum maximizes a measure of aggregate utility or welfare, whereas equimax lexicographically maximizes persons' utilities from smallest to largest. The paper analyzes conflicts among the criteria along with possibilities and pitfalls of achieving fair division in a variety of circumstances.

Suggested Citation

  • Steven J. Brams & Paul H. Edelman & Peter C. Fishburn, 2003. "Fair Division Of Indivisible Items," Theory and Decision, Springer, vol. 55(2), pages 147-180, September.
  • Handle: RePEc:kap:theord:v:55:y:2003:i:2:p:147-180
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    Citations

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    Cited by:

    1. Nicolò, Antonio & Yu, Yan, 2008. "Strategic divide and choose," Games and Economic Behavior, Elsevier, vol. 64(1), pages 268-289, September.
    2. Eric Budish & Estelle Cantillon, 2012. "The Multi-unit Assignment Problem: Theory and Evidence from Course Allocation at Harvard," American Economic Review, American Economic Association, vol. 102(5), pages 2237-2271, August.
    3. Eve Ramaekers, 2013. "Fair allocation of indivisible goods: the two-agent case," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 41(2), pages 359-380, July.
    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. Klamroth, Kathrin & Stiglmayr, Michael & Sudhoff, Julia, 2023. "Ordinal optimization through multi-objective reformulation," European Journal of Operational Research, Elsevier, vol. 311(2), pages 427-443.
    6. Caspari, Gian, 2020. "Booster draft mechanism for multi-object assignment," ZEW Discussion Papers 20-074, ZEW - Leibniz Centre for European Economic Research.
    7. Andreas Darmann & Christian Klamler, 2019. "Using the Borda rule for ranking sets of objects," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 53(3), pages 399-414, October.
    8. Steven J. Brams & William V. Gehrlein & Fred S. Roberts, 2022. "Peter C. Fishburn (1936–2021)," Theory and Decision, Springer, vol. 93(1), pages 1-6, July.
    9. Rudolf Vetschera & D. Marc Kilgour, 2013. "Strategic Behavior in Contested-Pile Methods for Fair Division of Indivisible Items," Group Decision and Negotiation, Springer, vol. 22(2), pages 299-319, March.
    10. RAMAEKERS, Eve, 2010. "Fair allocation of indivisible goods among two agents," LIDAM Discussion Papers CORE 2010087, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    11. Nhan-Tam Nguyen & Dorothea Baumeister & Jörg Rothe, 2018. "Strategy-proofness of scoring allocation correspondences for indivisible goods," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 50(1), pages 101-122, January.
    12. Brams, Steven J. & Kaplan, Todd R., 2017. "Dividing the indivisible: procedures for allocation cabinet ministries to political parties in a parlamentary system," Center for Mathematical Economics Working Papers 340, Center for Mathematical Economics, Bielefeld University.
    13. Steven Brams & D. Kilgour & Christian Klamler, 2012. "The undercut procedure: an algorithm for the envy-free division of indivisible items," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 39(2), pages 615-631, July.
    14. Haris Aziz, 2016. "A generalization of the AL method for fair allocation of indivisible objects," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 4(2), pages 307-324, October.
    15. Dall'Aglio, Marco & Mosca, Raffaele, 2007. "How to allocate hard candies fairly," Mathematical Social Sciences, Elsevier, vol. 54(3), pages 218-237, December.
    16. Rothe, Jörg & Schadrack, Hilmar & Schend, Lena, 2018. "Borda-induced hedonic games with friends, enemies, and neutral players," Mathematical Social Sciences, Elsevier, vol. 96(C), pages 21-36.

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