Fair Orientations: Proportionality and Equitability

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.