For One and All: Individual and Group Fairness in the Allocation of Indivisible Goods

Citation:

Scarlett J, Teh N, Zick Y. For One and All: Individual and Group Fairness in the Allocation of Indivisible Goods, in IJCAI 2021 Workshop on AI for Social Good. ; 2021.

Abstract:

Traditionally, research into the fair allocation of indivisible goods has focused on individual fairness and group fairness. In this paper, we explore the co-existence of individual envy-freeness (i-EF) and its group counterpart, group weighted envy-freeness (g-WEF). We propose several polynomial-time algorithms that can provably achieve i-EF and g-WEF simultaneously in various degrees of approximation under three different conditions on the agents’ valuation functions: (i) when agents have identical additive valuation functions, i-EFX and g-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 g-WEF1 in expectation. In addition, we introduce several novel fairness characterizations that exploit inherent group structures and their relation to individuals, such as proportional envy-freeness and group stability. We show that our algorithms can guarantee these properties approximately in polynomial time. Our results thus provide a first step into connecting individual and group fairness in the allocation of indivisible goods.