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Disputed Lands


  • Marco Dall'Aglio
  • Fabio Maccheroni


In this paper we consider the classical problem of dividing a land among many agents so that everybody is satisfied with the parcel she receives. In the literature, it is usually assumed that all the agents are endowed with cardinally comparable, additive, and monotone utility functions. In many economic and political situations violations of these assumptions may arise. We show how a family of cardinally comparable utility functions can be obtained starting directly from the agents’ preferences, and how a fair division of the land is feasible, without additivity or monotonicity requirements. Moreover, if the land to be divided can be modelled as a finite dimensional simplex, it is possible to obtain envy-free (and a fortiori fair) divisions of it into subsimplexes. The main tool is an extension of a representation theorem of Gilboa and Schmeidler (1989).

Suggested Citation

  • Marco Dall'Aglio & Fabio Maccheroni, 2007. "Disputed Lands," Carlo Alberto Notebooks 58, Collegio Carlo Alberto.
  • Handle: RePEc:cca:wpaper:58

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    References listed on IDEAS

    1. Francis Su, "undated". "Rental Harmony: Sperner's Lemma in Fair Division," Claremont Colleges Working Papers 1999-10, Claremont Colleges.
    2. Berliant, Marcus & Thomson, William & Dunz, Karl, 1992. "On the fair division of a heterogeneous commodity," Journal of Mathematical Economics, Elsevier, vol. 21(3), pages 201-216.
    3. Ichiishi, Tatsuro & Idzik, Adam, 1999. "Equitable allocation of divisible goods," Journal of Mathematical Economics, Elsevier, vol. 32(4), pages 389-400, December.
    4. L. Randall Wray & Stephanie Bell, 2004. "Introduction," Chapters,in: Credit and State Theories of Money, chapter 1 Edward Elgar Publishing.
    5. Berliant, Marcus & Dunz, Karl, 2004. "A foundation of location theory: existence of equilibrium, the welfare theorems, and core," Journal of Mathematical Economics, Elsevier, vol. 40(5), pages 593-618, August.
    6. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
    7. Fabio Maccheroni & Fabio Maccheroni & Massimo Marinacci & Massimo Marinacci, 2003. "How to cut a pizza fairly: Fair division with decreasing marginal evaluations," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 20(3), pages 457-465, June.
    8. Philippe Robert-Demontrond & R. Ringoot, 2004. "Introduction," Post-Print halshs-00081823, HAL.
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    Cited by:

    1. Farhad Hüsseinov & Nobusumi Sagara, 2013. "Existence of efficient envy-free allocations of a heterogeneous divisible commodity with nonadditive utilities," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 41(4), pages 923-940, October.
    2. Erel Segal-Halevi & Shmuel Nitzan, 2014. "Cake Cutting – Fair and Square," Working Papers 2014-01, Bar-Ilan University, Department of Economics.
    3. repec:eee:mateco:v:70:y:2017:i:c:p:1-28 is not listed on IDEAS

    More about this item


    Gender Fair Division; Envy-freeness; Preference Representation.;

    JEL classification:

    • D01 - Microeconomics - - General - - - Microeconomic Behavior: Underlying Principles
    • D74 - Microeconomics - - Analysis of Collective Decision-Making - - - Conflict; Conflict Resolution; Alliances; Revolutions

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