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How to Fairly Allocate Easy and Difficult Chores

Author

Listed:
  • Soroush Ebadian

    (DCS - Department of Computer Science [University of Toronto] - University of Toronto)

  • Dominik Peters

    (LAMSADE - Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision - Université Paris Dauphine-PSL - PSL - Université Paris Sciences et Lettres - CNRS - Centre National de la Recherche Scientifique)

  • Nisarg Shah

    (DCS - Department of Computer Science [University of Toronto] - University of Toronto)

Abstract

A major open question in fair allocation of indivisible items is whether there always exists an allocation of chores that is Pareto optimal (PO) and envy-free up to one item (EF1). We answer this question affirmatively for the natural class of bivalued utilities, where each agent partitions the chores into easy and difficult ones, and has cost > 1 for chores that are difficult for her and cost 1 for chores that are easy for her. Such an allocation can be found in polynomial time using an algorithm based on the Fisher market. We also show that for a slightly broader class of utilities, where each agent can have a potentially different integer , an allocation that is maximin share fair (MMS) always exists and can be computed in polynomial time, provided that each is an integer. Our MMS arguments also hold when allocating goods instead of chores, and extend to another natural class of utilities, namely weakly lexicographic utilities.

Suggested Citation

  • Soroush Ebadian & Dominik Peters & Nisarg Shah, 2022. "How to Fairly Allocate Easy and Difficult Chores," Post-Print hal-03834514, HAL.
    • Handle: RePEc:hal:journl:hal-03834514
    DOI: 10.5555/3535850.3535893
    Note: View the original document on HAL open archive server: https://hal.science/hal-03834514v1
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    References listed on IDEAS

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    1. Anna Bogomolnaia & Hervé Moulin & Fedor Sandomirskiy & Elena Yanovskaya, 2017. "Competitive Division of a Mixed Manna," Econometrica, Econometric Society, vol. 85(6), pages 1847-1871, November.
    2. Simina Br^anzei & Fedor Sandomirskiy, 2019. "Algorithms for Competitive Division of Chores," Papers 1907.01766, arXiv.org, revised Jul 2023.
    3. Eric Budish, 2011. "The Combinatorial Assignment Problem: Approximate Competitive Equilibrium from Equal Incomes," Journal of Political Economy, University of Chicago Press, vol. 119(6), pages 1061-1103.
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    Cited by:

    1. Camacho, Franklin & Fonseca-Delgado, Rigoberto & Pino Pérez, Ramón & Tapia, Guido, 2023. "Generalized binary utility functions and fair allocations," Mathematical Social Sciences, Elsevier, vol. 121(C), pages 50-60.
    2. Igarashi, Ayumi & Kawase, Yasushi & Suksompong, Warut & Sumita, Hanna, 2024. "Fair division with two-sided preferences," Games and Economic Behavior, Elsevier, vol. 147(C), pages 268-287.

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