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Fair allocation of indivisible goods with minimum inequality or minimum envy

Author

Listed:
  • Cornilly, Dries
  • Puccetti, Giovanni
  • Rüschendorf, Ludger
  • Vanduffel, Steven

Abstract

We provide a new mathematical framework for the classic problem of fair allocation of indivisible goods, showing that it can be formulated as the problem of finding an optimal column rearrangement of multiple matrices. Based on this formulation, we design two novel algorithms called MinCov and MinCovTarget to find optimal allocations under the newly introduced notion of minimum social inequality, and the popular notion of minimum envy. Numerical illustrations show an excellent performance of the newly developed algorithms also with respect to other allocation criteria, in particular for the maximum Nash welfare.

Suggested Citation

  • Cornilly, Dries & Puccetti, Giovanni & Rüschendorf, Ludger & Vanduffel, Steven, 2022. "Fair allocation of indivisible goods with minimum inequality or minimum envy," European Journal of Operational Research, Elsevier, vol. 297(2), pages 741-752.
    • Handle: RePEc:eee:ejores:v:297:y:2022:i:2:p:741-752
    DOI: 10.1016/j.ejor.2021.06.020
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    References listed on IDEAS

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    1. Thomson, William, 2011. "Chapter Twenty-One - Fair Allocation Rules," Handbook of Social Choice and Welfare, in: K. J. Arrow & A. K. Sen & K. Suzumura (ed.), Handbook of Social Choice and Welfare, edition 1, volume 2, chapter 21, pages 393-506, Elsevier.
    2. Hervé Moulin, 2019. "Fair Division in the Internet Age," Annual Review of Economics, Annual Reviews, vol. 11(1), pages 407-441, August.
    3. K. J. Arrow & A. K. Sen & K. Suzumura (ed.), 2011. "Handbook of Social Choice and Welfare," Handbook of Social Choice and Welfare, Elsevier, edition 1, volume 2, number 2.
    4. Jérôme Lang & Jörg Rothe, 2016. "Fair Division of Indivisible Goods," Springer Texts in Business and Economics, in: Jörg Rothe (ed.), Economics and Computation, edition 1, chapter 0, pages 493-550, Springer.
    5. Kilgour, D. Marc & Vetschera, Rudolf, 2018. "Two-player fair division of indivisible items: Comparison of algorithms," European Journal of Operational Research, Elsevier, vol. 271(2), pages 620-631.
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