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Efficient Fair Division

Author

Listed:
  • Steven J. Brams

    (New York University, steven.brams@nyu.edu)

  • Daniel L. King

    (Sarah Lawrence College, dking@mail.slc.edu)

Abstract

Two or more players rank a set of indivisible items from best to worst. An efficient allocation of items is characterized, which may satisfy such properties as maximin, Borda maximin, and envy-avoidance. Whereas the two maximin properties are in conflict with envy-avoidance, there is always an efficient allocation that does not ensure envy, but it may not be maximin or Borda maximin. Computer calculations show that maximin allocations lead to envy quite often, but Borda maximin allocations do so only rarely. Implications of the theoretical findings for real-world fair-division problems are discussed.

Suggested Citation

  • Steven J. Brams & Daniel L. King, 2005. "Efficient Fair Division," Rationality and Society, , vol. 17(4), pages 387-421, November.
    • Handle: RePEc:sae:ratsoc:v:17:y:2005:i:4:p:387-421
    DOI: 10.1177/1043463105058317
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    References listed on IDEAS

    as
    1. Steven J. Brams & Peter C. Fishburn, 2000. "Fair division of indivisible items between two people with identical preferences: Envy-freeness, Pareto-optimality, and equity," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 17(2), pages 247-267.
    2. Edelman, Paul & Fishburn, Peter, 2001. "Fair division of indivisible items among people with similar preferences," Mathematical Social Sciences, Elsevier, vol. 41(3), pages 327-347, May.
    3. Carmen BeviÂ, 1998. "Fair allocation in a general model with indivisible goods," Review of Economic Design, Springer;Society for Economic Design, vol. 3(3), pages 195-213.
    4. Steven J. Brams & Todd R. Kaplan, 2004. "Dividing the Indivisible," Journal of Theoretical Politics, , vol. 16(2), pages 143-173, April.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
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    Cited by:

    1. Steven J. Brams & D. Marc Kilgour & Christian Klamler, 2017. "Maximin Envy-Free Division of Indivisible Items," Group Decision and Negotiation, Springer, vol. 26(1), pages 115-131, January.
    2. Brams, Steven J. & Kilgour, D. Marc & Klamler, Christian, 2014. "An algorithm for the proportional division of indivisible items," MPRA Paper 56587, University Library of Munich, Germany.
    3. Brams, Steven J. & Kilgour, D. Marc & Klamler, Christian, 2013. "Two-Person Fair Division of Indivisible Items: An Efficient, Envy-Free Algorithm," MPRA Paper 47400, University Library of Munich, Germany.
    4. 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.
    5. Onur Kesten & Ayşe Yazıcı, 2012. "The Pareto-dominant strategy-proof and fair rule for problems with indivisible goods," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 50(2), pages 463-488, June.
    6. 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).
    7. Andreas Darmann & Christian Klamler, 2016. "Proportional Borda allocations," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 47(3), pages 543-558, October.
    8. 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.
    9. 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.
    10. 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.
    11. Dall'Aglio, Marco & Mosca, Raffaele, 2007. "How to allocate hard candies fairly," Mathematical Social Sciences, Elsevier, vol. 54(3), pages 218-237, December.
    12. 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.
    13. Cechlárová, Katarína & Fleiner, Tamás, 2017. "Pareto optimal matchings with lower quotas," Mathematical Social Sciences, Elsevier, vol. 88(C), pages 3-10.
    14. Steven J. Brams & D. Marc Kilgour & Christian Klamler, 2022. "Two-Person Fair Division of Indivisible Items when Envy-Freeness is Impossible," SN Operations Research Forum, Springer, vol. 3(2), pages 1-23, June.
    15. Brams, Steven & Kilgour, D. Marc & Klamler, Christian, 2014. "How to divide things fairly," MPRA Paper 58370, University Library of Munich, Germany.
    16. Katarina Cechlarova & Bettina Klaus & David F.Manlove, 2018. "Pareto optimal matchings of students to courses in the presence of prerequisites," Cahiers de Recherches Economiques du Département d'économie 16.04, Université de Lausanne, Faculté des HEC, Département d’économie.
    17. 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.
    18. 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.
    19. Fedor Sandomirskiy & Erel Segal-Halevi, 2019. "Efficient Fair Division with Minimal Sharing," Papers 1908.01669, arXiv.org, revised Apr 2022.
    20. Kilgour, D. Marc & Vetschera, Rudolf, 2018. "Two-player fair division of indivisible items: Comparison of algorithms," European Journal of Operational Research, Elsevier, vol. 271(2), pages 620-631.

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