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Maximin Envy-Fee Division of Indivisible Items

28 Pages Posted: 25 Mar 2015  

Steven J. Brams

New York University (NYU) - Wilf Family Department of Politics

D. Marc Kilgour

Wilfrid Laurier University

Christian Klamler

University of Graz

Date Written: March 2015

Abstract

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

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

Steven J. Brams (Contact Author)

New York University (NYU) - Wilf Family Department of Politics ( email )

Dept. of Politics
19 West 4th St., 2nd Fl.
New York, NY 10012
United States
212-998-8510 (Phone)
212-995-4184 (Fax)

HOME PAGE: http://politics.as.nyu.edu/object/stevenbrams.html

D. Marc Kilgour

Wilfrid Laurier University ( email )

75 University Ave W
Waterloo, Ontario N2L 3C5
Canada
519-884-0710 Ext.4208 (Phone)
519-884-5057 (Fax)

Christian Klamler

University of Graz ( email )

Graz
Austria

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