28 Pages Posted: 25 Mar 2015
Date Written: March 2015
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.
Keywords: Fair division, indivisible items, maximin, envy-free
JEL Classification: C70, D63
Suggested Citation: Suggested Citation
Brams, Steven J. and Kilgour, D. Marc and Klamler, Christian, Maximin Envy-Fee Division of Indivisible Items (March 2015). Available at SSRN: https://ssrn.com/abstract=2584131 or http://dx.doi.org/10.2139/ssrn.2584131