是选择EFX还是MMS，这是个问题
To EFX OR to MMS, That is the Question
- Pennsylvania State University（宾夕法尼亚州立大学）
- IIT Delhi（德里印度理工学院）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
该研究探讨了不可分割物品的EFX与MMS公平性概念的智能体层面析取，构造了相关不可能性反例，证明了特定条件下的存在性结果并明确了其与组成部分的区分。
AI中文摘要：
我们研究了不可分割物品的两个核心公平性概念的智能体层面析取，即每个智能体必须满足无嫉妒至多任何物品（EFX）或最大最小份额（MMS）。人们可能期望这种灵活性能恢复存在性，尤其是因为EFX本身的存在性已困扰了近十年未解决。令人惊讶的是，它并未恢复存在性。我们构造了反例，涉及3个智能体和8个子模块物品，以及3个智能体和7个子模块负物品，显著强化了近期的EFX不可能性结果。从积极方面看，我们证明了加法混合物品的存在性，当最多有3种估值类型且其中一种类型为单元素时成立。我们的证明可扩展到物品的加法之外，并为物品和3智能体负物品实例产生近似方案。我们还明确了该析取与其组成部分之间的清晰区分：对于具有2种估值类型的加法负物品，已知EFX和MMS均不成立，而EFX∨MMS分配总是存在。最后，我们表明相同的加法估值甚至对于混合物品也允许合取EFX∧MMS。总体而言，我们的结果表明，允许在选择智能体特定公平性证书方面的灵活性拓展了公平解决方案的边界，同时也揭示了令人惊讶的不可能性。
英文摘要：
We study the agent-wise disjunction of two central fairness notions for indivisible items, where every agent must be either envy-free up to any item (EFX) or maximin-share (MMS) satisfied. One might expect that having a flexible fairness requirement for individual agents will restore existence, especially because the existence of EFX itself resisted resolution for nearly a decade. Surprisingly, it does not. We construct counterexamples with three agents and eight submodular goods, and with three agents and seven submodular chores, significantly strengthening recent EFX impossibility results. On the positive side, we prove existence for additive mixed items with at most three valuation types when one type is a singleton. Additionally, we obtain polynomial-time approximation schemes for additive goods-only and chores-only instances. We also identify a clean separation between the disjunction and its constituents: For additive chores with two valuation types, EFX and MMS are both known to fail, whereas an EFX $\vee$ MMS allocation always exists. Finally, we show that identical additive valuations even admit the conjunction EFX $\wedge$ MMS for mixed items. Overall, our results show that allowing flexibility in choosing agent-specific fairness certificates expands the frontier of fair solutions while also uncovering surprising impossibilities.
