发表机构
Penn State University; Rutgers University（宾夕法尼亚州立大学; 罗格斯大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究无嫉妒性与公平性两种公平概念的兼容性，明确两类场景下同时满足对应松弛分配的存在性与复杂性，提出算法并首次探究跨概念事前-事后保证。
AI 中文摘要
公平分配领域的近期研究要么聚焦于同时满足密切相关的公平性概念，要么在事前和事后场景中实现单一公平性概念。本文研究两种根本不同的公平性概念——无嫉妒性（envy-freeness）与公平性（equitability）的兼容性，针对仅含不可分物品的场景和仅含不可分劳役的场景，探讨同时满足其松弛版本的存在性与复杂性，揭示两类场景间的显著差异。研究表明，即使对于归一化加性估值，EF1+EQ1分配也可能不存在；核心算法结果是，对于归一化二元物品，最多7个代理时可计算出EF1+EQ1分配，而与之形成鲜明对比的是，二元劳役在任意数量代理下均可满足更强的EFX+EQX保证，且无需归一化。本文还首次开展跨概念事前-事后保证的研究，探究随机分配能否为一种概念提供事前保证，同时保留另一种概念的事后保证。
英文摘要
Recent work in fair division has focused on either simultaneously satisfying closely related fairness notions or achieving a single notion across the ex-ante and ex-post worlds. We study the compatibility of two fundamentally different fairness notions: envy-freeness and equitability. For indivisible goods-only and chores-only settings, we study the existence and complexity of simultaneously satisfying their relaxations, revealing sharp contrasts between the two settings. For normalized binary goods, we give a polynomial-time algorithm for computing an EF1+EQ1 allocation with at most seven agents, but also construct a normalized instance with a larger number of agents for which no such allocation exists. In sharp contrast, binary chores admit the stronger EFX+EQX guarantee for any number of agents, even without normalization. We further initiate the study of cross-notion ex-ante and ex-post guarantees, asking whether randomized allocations can provide ex-ante guarantees for one notion while preserving ex-post guarantees for another.
Comments43 pages
