Fair allocation of indivisible goods is a well-explored problem. Traditionally, research focused on individual fairness - are individual agents satisfied with their allotted share? - and group fairness - are groups of agents treated fairly? In this paper, we explore the coexistence of individual envy-freeness (i-EF) and its group counterpart, group weighted envy-freeness (g-WEF), in the allocation of indivisible goods. We propose several polynomial-time algorithms that provably achieve i-EF and g-WEF simultaneously in various degrees of approximation under three different conditions on the agents' (i) when agents have identical additive valuation functions, i-EFX and i-WEF1 can be achieved simultaneously; (ii) when agents within a group share a common valuation function, an allocation satisfying both i-EF1 and g-WEF1 exists; and (iii) when agents' valuations for goods within a group differ, we show that while maintaining i-EF1, we can achieve a 1/3-approximation to ex-ante g-WEF1. Our results thus provide a first step towards connecting individual and group fairness in the allocation of indivisible goods, in hopes of its useful application to domains requiring the reconciliation of diversity with individual demands.

翻译：不可分物品的公平分配是一个已被充分研究的问题。传统上，研究关注个体公平——个体代理人对其分配份额是否满意？——以及群体公平——代理人群体是否受到公平对待？本文探讨了在不可分物品分配中，个体无嫉妒性（i-EF）及其群体对应概念——群体加权无嫉妒性（g-WEF）的共存问题。我们提出了若干多项式时间算法，在三种不同条件下，以不同程度的近似性同时实现i-EF和g-WEF：（i）当代理人具有相同的可加效用函数时，可同时实现i-EFX和i-WEF1；（ii）当群体内代理人共享共同的效用函数时，存在同时满足i-EF1和g-WEF1的分配方案；（iii）当群体内代理人对物品的估值不同时，我们证明在保持i-EF1的同时，可实现对事前g-WEF1的1/3近似。因此，我们的结果为连接不可分物品分配中的个体公平与群体公平迈出了第一步，期望能应用于需要调和多样性与个体需求的领域。