Equity; Fairness; Health-Delivery Optimization; Outcome Constraints; Resource Allocation
Vertical equity or fairness is an important aspect in many settings, yet has received relatively little attention in the literature. Recent developments underline the practical relevance (e.g., COVID-19 vaccination policies).It plays an important role in the performance evaluation of many (nongovernmental) organizations. For example, donors might require a family-planning organization to allocate a minimum fraction of the total utility (client volume) to a particular player (the “high-impact” subgroup of the population, e.g., young and poor clients). However, the price (decrease in client volume) of such requirements is not well-understood. Consequently, this price is not accounted for in decision making.The authors provide an analytical upper bound on the price (i.e., loss of overall utility) of vertical equity considerations in resource allocation. The authors assume that these concerns are expressed via outcome constraints, specifying a minimum percentage of the total utility for each player. Their set-up considers a decision maker maximizing total utility over a general convex set, subject to outcome constraints. The set-up is general and applicable to many practical problems.The authors' results depend only on high-level parameters and are therefore well-suited for strategic decision making.The authors conclude with two applications. First, the authors apply their results to practical instances in health delivery. They confirm that outcome constraints can entail a substantial price and analyze the factors driving this price close to the worst-case bound. Second, the authors analyze how their results can help bound the impact of prioritization in vaccine allocation.