Fair Orientations: Proportionality and Equitability

TL;DR

This paper explores fair allocation methods for indivisible items with relevance constraints, extending fairness criteria beyond envy-freeness to include proportionality and equitability, and analyzes their existence and computational complexity.

Contribution

It introduces fairness criteria like proportionality and equitability under relevance constraints, and studies their existence and computational complexity in diverse settings.

Findings

Existence results for proportionality and equitability under relevance constraints.

Complexity classifications for computing fair allocations.

Extensions to settings with goods, chores, or mixed items.

Abstract

We study the fair allocation of indivisible items under relevance constraints, where each agent has a set of relevant items and can only receive items that are relevant to them. While the relevance constraint has been studied in recent years, existing work has largely focused on envy-freeness. Our work extends this study to other key fairness criteria -- such as proportionality, equitability, and their relaxations -- in settings where the items may be goods, chores, or a mixture of both. We complement the literature by presenting a picture of the existence and computational complexity of the considered criteria.