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Fair Division with Binary Valuations: One Rule to Rule Them All

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Web and Internet Economics (WINE 2020)

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 12495))

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Abstract

We study fair allocation of indivisible goods among agents. Prior research focuses on additive agent preferences, which leads to an impossibility when seeking truthfulness, fairness, and efficiency. We show that when agents have binary additive preferences, a compelling rule—maximum Nash welfare (MNW)—provides all three guarantees. Specifically, we show that deterministic MNW with lexicographic tie-breaking is group strategyproof in addition to being envy-free up to one good and Pareto optimal. We also prove that fractional MNW—known to be group strategyproof, envy-free, and Pareto optimal—can be implemented as a distribution over deterministic MNW allocations, which are envy-free up to one good. Our work establishes maximum Nash welfare as the ultimate allocation rule in the realm of binary additive preferences.

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Notes

  1. 1.

    There are two popular definitions of EFX [3]; this result holds for the stronger one: an allocation is EFX if the envy that one agent has toward another can be eliminated by removing any good from the envied agent’s bundle.

  2. 2.

    There are two popular definitions of EFX [3]. The original definition by Caragiannis et al. [16] asks that agent i not envy agent j after removal of any good from agent j’s bundle that has positive value for agent i, whereas a latter definition omits the requirement of “positive value”. Under binary additive valuations, the former definition is equivalent to EF1 whereas the latter definition is stronger than EF1.

  3. 3.

    We note that tie-breaking by agent index is without loss of generality. One can break ties according to any given ordering of the agents, and the corresponding rule will still satisfy all the desiderata.

  4. 4.

    In case of Pareto optimality of a fractional allocation, we require that no other fractional allocation Pareto-dominate it.

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Author information

Authors and Affiliations

  1. Harvard University, Cambridge, USA

    Daniel Halpern & Ariel D. Procaccia

  2. Purdue University, West Lafayette, USA

    Alexandros Psomas

  3. University of Toronto, Toronto, Canada

    Nisarg Shah

Authors
  1. Daniel Halpern
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  2. Ariel D. Procaccia
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  3. Alexandros Psomas
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  4. Nisarg Shah
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Corresponding author

Correspondence to Alexandros Psomas .

Editor information

Editors and Affiliations

  1. Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China

    Xujin Chen

  2. Shanghai University of Finance and Economics, Shanghai, China

    Nikolai Gravin

  3. Goethe University Frankfurt, Frankfurt am Main, Germany

    Martin Hoefer

  4. University of Illinois at Urbana-Champaign, Urbana, IL, USA

    Ruta Mehta

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Halpern, D., Procaccia, A.D., Psomas, A., Shah, N. (2020). Fair Division with Binary Valuations: One Rule to Rule Them All. In: Chen, X., Gravin, N., Hoefer, M., Mehta, R. (eds) Web and Internet Economics. WINE 2020. Lecture Notes in Computer Science(), vol 12495. Springer, Cham. https://doi.org/10.1007/978-3-030-64946-3_26

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  • DOI: https://doi.org/10.1007/978-3-030-64946-3_26

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