The Unreasonable Fairness of Maximum Nash Welfare

Caragiannis, I., Kurokawa, D., Moulin, H. , Procaccia, A. D., Shah, N. and Wang, J. (2016) The Unreasonable Fairness of Maximum Nash Welfare. In: EC '16 17th ACM Conference on Economics and Computation, Maastricht, The Netherlands, 24-28 Jul 2016, pp. 305-322. ISBN 9781450339360 (doi: 10.1145/2940716.2940726)

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 unexpectedly, 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 lead us to believe that MNW is the ultimate solution for allocating indivisible goods, and underlie its deployment on a popular fair division website.

• Item Type: Conference Proceedings
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Moulin, Professor Herve
• Authors: Caragiannis, I., Kurokawa, D., Moulin, H., Procaccia, A. D., Shah, N., and Wang, J.
• College/School: College of Social Sciences > Adam Smith Business School > Economics
• ISBN: 9781450339360
• Copyright Holders: Copyright © 2016 The Authors
• First Published: First published in EC '16 Proceedings of the 2016 ACM Conference on Economics and Computation: 305-322
• Publisher Policy: Reproduced in accordance with the publisher copyright policy

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