Harm Ratio: A Novel and Versatile Fairness Criterion

Abstract: Envy-freeness has become the cornerstone of fair division research. In settings where each individual is allocated a disjoint share of collective resources, it is a compelling fairness axiom which demands that no individual strictly prefer the allocation of another individual to their own. Unfortunately, in many real-life collective decision-making problems, the goal is to choose a (common) public outcome that is equally applicable to all individuals, and the notion of envy becomes vacuous. Consequently, this literature has avoided studying fairness criteria that focus on individuals feeling a sense of jealousy or resentment towards other individuals (rather than towards the system), missing out on a key aspect of fairness. In this work, we propose a novel fairness criterion, individual harm ratio, which is inspired by envy-freeness but applies to a broad range of collective decision-making settings. Theoretically, we identify minimal conditions under which this criterion and its groupwise extensions can be guaranteed, and study the computational complexity of related problems. Empirically, we conduct experiments with real data to show that our fairness criterion is powerful enough to differentiate between prominent decision-making algorithms for a range of tasks from voting and fair division to participatory budgeting and peer review.