Fair Division of Indivisible Items: Envy-Freeness vs. Efficiency Revisited

We study conflicts between envy-based fairness and efficiency for allocating indivisible items under additive utilities. We formalize several small, transparent instances showing that standard envy-freeness (EF) or its relaxations EFX and EFX0—i.e., envy-freeness up to any item, where EFX restricts attention to positively valued items and EFX0 allows removing zero-valued items as well—can conflict with Pareto-optimality (PO), maximin (MM), or maximum Nash welfare (MNW). Normatively, we argue that envy-freeness (even as EFX or EFX0) is not a panacea for allocating indivisible items and should be weighed against efficiency and welfare criteria.