Group Decision and Negotiation

, Volume 26, Issue 1, pp 115–131

Maximin Envy-Free Division of Indivisible Items

  • Steven J. Brams
  • D. Marc Kilgour
  • Christian Klamler


Assume that two players have strict rankings over an even number of indivisible items. We propose two algorithms to find balanced allocations of these items that are maximin—maximize the minimum rank of the items that the players receive—and are envy-free and Pareto-optimal, if such allocations exist. To determine whether an envy-free allocation exists, we introduce a simple condition on preference profiles; in fact, our condition guarantees the existence of a maximin, envy-free, and Pareto-optimal allocation. Although not strategy-proof, our algorithms would be difficult to manipulate unless a player has complete information about its opponent’s ranking. We assess the applicability of the algorithms to real-world problems, such as allocating marital property in a divorce or assigning people to committees or projects.


Fair division Allocation of indivisible items Envy-freeness Maximin 

Copyright information

© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  • Steven J. Brams
    • 1
  • D. Marc Kilgour
    • 2
  • Christian Klamler
    • 3
  1. 1.Department of PoliticsNew York UniversityNew YorkUSA
  2. 2.Department of MathematicsWilfrid Laurier UniversityWaterlooCanada
  3. 3.Institute of Public EconomicsUniversity of GrazGrazAustria

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