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The Unreasonable Fairness of Maximum Nash Welfare

Authors:

Ioannis Caragiannis,

David Kurokawa,

Herv� Moulin,

Ariel D. Procaccia,

Junxing WangAuthors Info & Claims

ACM Transactions on Economics and Computation (TEAC), Volume 7, Issue 3

Article No.: 12, Pages 1 - 32

https://doi.org/10.1145/3355902

Published: 24 September 2019 Publication History

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Abstract

The maximum Nash welfare (MNW) solution—which selects an allocation that maximizes the product of utilities—is known to provide outstanding fairness guarantees when allocating divisible goods. And while it seems to lose its luster when applied to indivisible goods, we show that, in fact, the MNW solution is strikingly fair even in that setting. In particular, we prove that it selects allocations that are envy-free up to one good—a compelling notion that is quite elusive when coupled with economic efficiency. We also establish that the MNW solution provides a good approximation to another popular (yet possibly infeasible) fairness property, the maximin share guarantee, in theory and—even more so—in practice. While finding the MNW solution is computationally hard, we develop a nontrivial implementation and demonstrate that it scales well on real data. These results establish MNW as a compelling solution for allocating indivisible goods and underlie its deployment on a popular fair-division website.

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Teh NDastani MSichman JAlechina NDignum V(2024)Distributive and Temporal Fairness in Algorithmic Collective Decision-MakingProceedings of the 23rd International Conference on Autonomous Agents and Multiagent Systems10.5555/3635637.3663284(2779-2781)Online publication date: 6-May-2024
https://dl.acm.org/doi/10.5555/3635637.3663284
Viswanathan MMehta RDastani MSichman JAlechina NDignum V(2024)On the existence of EFX under picky or non-differentiative agentsProceedings of the 23rd International Conference on Autonomous Agents and Multiagent Systems10.5555/3635637.3663218(2534-2536)Online publication date: 6-May-2024
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Index Terms

The Unreasonable Fairness of Maximum Nash Welfare
1. Applied computing
  1. Law, social and behavioral sciences
    1. Economics
2. Theory of computation
  1. Theory and algorithms for application domains
    1. Algorithmic game theory and mechanism design
      1. Algorithmic mechanism design

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cover image ACM Transactions on Economics and Computation

ACM Transactions on Economics and Computation Volume 7, Issue 3

Special Issue on EC'16

August 2019

147 pages

ISSN:2167-8375

EISSN:2167-8383

DOI:10.1145/3364621

Editors:
David Pennock
Microsoft
,
Ilya Segal
Stanford University

Issue’s Table of Contents

Copyright © 2019 ACM.

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Publication History

Published: 24 September 2019

Accepted: 01 June 2018

Revised: 01 October 2017

Received: 01 January 2017

Published in TEAC Volume 7, Issue 3

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Sloan Research Fellowship
NSERC under the Discovery Grants program
COST Action IC1205 on “Computational Social Choice”
University of Patras
Caratheodory research
National Science Foundation

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Cited By

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https://doi.org/10.1016/j.ipl.2024.106519
Teh NDastani MSichman JAlechina NDignum V(2024)Distributive and Temporal Fairness in Algorithmic Collective Decision-MakingProceedings of the 23rd International Conference on Autonomous Agents and Multiagent Systems10.5555/3635637.3663284(2779-2781)Online publication date: 6-May-2024
https://dl.acm.org/doi/10.5555/3635637.3663284
Viswanathan MMehta RDastani MSichman JAlechina NDignum V(2024)On the existence of EFX under picky or non-differentiative agentsProceedings of the 23rd International Conference on Autonomous Agents and Multiagent Systems10.5555/3635637.3663218(2534-2536)Online publication date: 6-May-2024
https://dl.acm.org/doi/10.5555/3635637.3663218
Kawase YRoy BSanpui MDastani MSichman JAlechina NDignum V(2024)Contiguous Allocation of Binary Valued Indivisible Items on a PathProceedings of the 23rd International Conference on Autonomous Agents and Multiagent Systems10.5555/3635637.3663149(2327-2329)Online publication date: 6-May-2024
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Cohen SAgmon NDastani MSichman JAlechina NDignum V(2024)Near-Optimal Online Resource Allocation in the Random-Order ModelProceedings of the 23rd International Conference on Autonomous Agents and Multiagent Systems10.5555/3635637.3663113(2219-2221)Online publication date: 6-May-2024
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Aloisio ABil� VCaruso AFlammini MVinci CDastani MSichman JAlechina NDignum V(2024)Approximately Fair Allocation of Indivisible Items with Random ValuationsProceedings of the 23rd International Conference on Autonomous Agents and Multiagent Systems10.5555/3635637.3663080(2120-2122)Online publication date: 6-May-2024
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Sun ALi BDastani MSichman JAlechina NDignum V(2024)Allocating Contiguous Blocks of Indivisible Chores Fairly: RevisitedProceedings of the 23rd International Conference on Autonomous Agents and Multiagent Systems10.5555/3635637.3663042(1800-1808)Online publication date: 6-May-2024
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Li ZLiu SLu XTao BTao YDastani MSichman JAlechina NDignum V(2024)A Complete Landscape for the Price of Envy-FreenessProceedings of the 23rd International Conference on Autonomous Agents and Multiagent Systems10.5555/3635637.3662975(1183-1191)Online publication date: 6-May-2024
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Hummel HIgarashi ADastani MSichman JAlechina NDignum V(2024)Keeping the Harmony Between Neighbors: Local Fairness in Graph Fair DivisionProceedings of the 23rd International Conference on Autonomous Agents and Multiagent Systems10.5555/3635637.3662939(852-860)Online publication date: 6-May-2024
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Caragiannis IHansen KRathi NDastani MSichman JAlechina NDignum V(2024)On the Complexity of Pareto-Optimal and Envy-Free LotteriesProceedings of the 23rd International Conference on Autonomous Agents and Multiagent Systems10.5555/3635637.3662872(244-252)Online publication date: 6-May-2024
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