Asymptotic Fair Division: Chores Are Easier Than Goods
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866910921802121216 |
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| author | Manurangsi, Pasin Suksompong, Warut |
| author_facet | Manurangsi, Pasin Suksompong, Warut |
| contents | When dividing items among agents, two of the most widely studied fairness notions are envy-freeness and proportionality. We consider a setting where $m$ chores are allocated to $n$ agents and the disutility of each chore for each agent is drawn from a probability distribution. We show that an envy-free allocation exists with high probability provided that $m \ge 2n$, and moreover, $m$ must be at least $n+Θ(n)$ in order for the existence to hold. On the other hand, we prove that a proportional allocation is likely to exist as long as $m = ω(1)$, and this threshold is asymptotically tight. Our results reveal a clear contrast with the allocation of goods, where a larger number of items is necessary to ensure existence for both notions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_20704 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Asymptotic Fair Division: Chores Are Easier Than Goods Manurangsi, Pasin Suksompong, Warut Computer Science and Game Theory Probability When dividing items among agents, two of the most widely studied fairness notions are envy-freeness and proportionality. We consider a setting where $m$ chores are allocated to $n$ agents and the disutility of each chore for each agent is drawn from a probability distribution. We show that an envy-free allocation exists with high probability provided that $m \ge 2n$, and moreover, $m$ must be at least $n+Θ(n)$ in order for the existence to hold. On the other hand, we prove that a proportional allocation is likely to exist as long as $m = ω(1)$, and this threshold is asymptotically tight. Our results reveal a clear contrast with the allocation of goods, where a larger number of items is necessary to ensure existence for both notions. |
| title | Asymptotic Fair Division: Chores Are Easier Than Goods |
| topic | Computer Science and Game Theory Probability |
| url | https://arxiv.org/abs/2504.20704 |