Caragiannis, I., Kurokawa, D., Moulin, H. , Procaccia, A. D., Shah, N. and Wang, J. (2019) The unreasonable fairness of maximum Nash welfare. ACM Transactions on Economics and Computation, 7(3), 12. (doi: 10.1145/3355902)
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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.
| Item Type: | Articles |
|---|---|
| Additional Information: | This work was supported in part by the National Science Foundation under grants IIS-1350598, CCF-1215883, and CCF-1525932; by a Sloan Research Fellowship; by the COST Action IC1205 on “Computational Social Choice”; by the Caratheodory research grant E.114 from the University of Patras; and by the NSERC under the Discovery Grants program. |
| 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 |
| Journal Name: | ACM Transactions on Economics and Computation |
| Publisher: | ACM |
| ISSN: | 2167-8375 |
| ISSN (Online): | 2167-8375 |
| Published Online: | 24 September 2019 |
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