A Just Approach Balancing Rawlsian Leximax Fairness and Utilitarianism

Numerous AI-assisted resource allocation decisions need to balance the conflicting goals of fairness and efficiency. Our paper studies the challenging task of defining and modeling a proper fairness-efficiency trade off. We define fairness with Rawlsian leximax fairness, which views the lexicographic maximum among all feasible outcomes as the most equitable; and define efficiency with Utilitarianism, which seeks to maximize the sum of utilities received by entities regardless of individual differences. Motivated by a justice-driven trade off principle: prioritize fairness to benefit the less advantaged unless too much efficiency is sacrificed, we propose a sequential optimization procedure to balance leximax fairness and utilitarianism in decision-making. Each iteration of our approach maximizes a social welfare function, and we provide a practical mixed integer/linear programming (MILP) formulation for each maximization problem. We illustrate our method on a budget allocation example. Compared with existing approaches of balancing equity and efficiency, our method is more interpretable in terms of parameter selection, and incorporates a strong equity criterion with a thoroughly balanced perspective.