Article on Maximin Envy-Free Division of Indivisible Items

Steven J. Brams (New York University (NYU) – Wilf Family Department of Politics), D. Marc Kilgour (Wilfrid Laurier University) & Christian Klamler (University of Graz) recently published an article entitled, Maximin Envy-Free Division of Indivisible Items, March 2015. Provided below is the abstract from SSRN:

Assume that two players have strict rankings over an even number of indivisible items. We propose algorithms to find 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. We show that neither maximin nor envy-free allocations may satisfy other criteria of fairness, such as Borda maximinality. Although not strategy-proof, the 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.