On the Fairness of Additive Welfarist Rules
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866912937769172992 |
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| author | Celine, Karen Frilya Suksompong, Warut Yuen, Sheung Man |
| author_facet | Celine, Karen Frilya Suksompong, Warut Yuen, Sheung Man |
| contents | Allocating indivisible goods is a ubiquitous task in fair division. We study additive welfarist rules, an important class of rules which choose an allocation that maximizes the sum of some function of the agents' utilities. Prior work has shown that the maximum Nash welfare (MNW) rule is the unique additive welfarist rule that guarantees envy-freeness up to one good (EF1). We strengthen this result by showing that MNW remains the only additive welfarist rule that ensures EF1 for identical-good instances, two-value instances, as well as normalized instances with three or more agents. On the other hand, if the agents' utilities are integers, we demonstrate that several other rules offer the EF1 guarantee, and provide characterizations of these rules for various classes of instances. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_15472 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the Fairness of Additive Welfarist Rules Celine, Karen Frilya Suksompong, Warut Yuen, Sheung Man Computer Science and Game Theory Theoretical Economics Allocating indivisible goods is a ubiquitous task in fair division. We study additive welfarist rules, an important class of rules which choose an allocation that maximizes the sum of some function of the agents' utilities. Prior work has shown that the maximum Nash welfare (MNW) rule is the unique additive welfarist rule that guarantees envy-freeness up to one good (EF1). We strengthen this result by showing that MNW remains the only additive welfarist rule that ensures EF1 for identical-good instances, two-value instances, as well as normalized instances with three or more agents. On the other hand, if the agents' utilities are integers, we demonstrate that several other rules offer the EF1 guarantee, and provide characterizations of these rules for various classes of instances. |
| title | On the Fairness of Additive Welfarist Rules |
| topic | Computer Science and Game Theory Theoretical Economics |
| url | https://arxiv.org/abs/2412.15472 |