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

TL;DR

This paper investigates the coexistence of individual and group fairness in allocating indivisible goods, proposing algorithms that achieve various fairness criteria simultaneously under different valuation conditions.

Contribution

It introduces polynomial-time algorithms that achieve combined individual and group fairness in various settings of agent valuation functions.

Findings

Algorithms achieve i-EF and g-WEF simultaneously in specific valuation scenarios.

Existence of allocations satisfying both i-EF1 and g-WEF1 when agents within a group share valuations.

A 1/3-approximation to ex-ante g-WEF1 while maintaining i-EF1 in diverse valuation settings.

Abstract

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.