Fair allocation of indivisible goods with minimum inequality or minimum envy criteria

European Journal of Operational Research

27 Pages Posted: 2 Jan 2020 Last revised: 11 Jun 2021

See all articles by Dries Cornilly

Dries Cornilly

Asteria Investment Managers

Giovanni Puccetti

University of Milan - Department of Economics, Management and Quantitative Methods (DEMM)

Ludger Rüschendorf

University of Freiburg

Steven Vanduffel

Vrije Universiteit Brussel (VUB)

Date Written: 2021

Abstract

For the classic problem of fair allocation of indivisible goods, we introduce the notion of minimum social inequality allocations and discuss its connection to other fair allocation rules such as minimum envy. We show that a fair allocation problem can always be cast as the problem of finding an optimal rearrangement of multiple matrices. Based on this reformulation, we provide two novel algorithms to find allocations with a minimum level of social inequality or with a minimum level of envy. Numerical illustrations show the efficiency of the newly developed algorithms, especially in problems with a large number of objects/agents.

Keywords: Decision analysis, fair allocation of indivisible goods, minimum envy.

Suggested Citation

Cornilly, Dries and Puccetti, Giovanni and Rüschendorf, Ludger and Vanduffel, Steven, Fair allocation of indivisible goods with minimum inequality or minimum envy criteria (2021). European Journal of Operational Research, Available at SSRN: https://ssrn.com/abstract=3512113 or http://dx.doi.org/10.2139/ssrn.3512113

Dries Cornilly

Asteria Investment Managers ( email )

Rue du Rhône 62
Geneva, 1204
Switzerland

Giovanni Puccetti

University of Milan - Department of Economics, Management and Quantitative Methods (DEMM) ( email )

Via Conservatorio, 7
Milan, 20122
Italy

Ludger Rüschendorf

University of Freiburg ( email )

Fahnenbergplatz
Freiburg, D-79085
Germany

Steven Vanduffel (Contact Author)

Vrije Universiteit Brussel (VUB) ( email )

Pleinlaan 2
Brussels, Brabant 1050
Belgium

HOME PAGE: http://www.stevenvanduffel.com

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