Balancing Lexicographic Fairness and a Utilitarian Objective with Application to Kidney Exchange
This work addresses fairness-efficiency trade-offs in kidney exchange, an incremental improvement with practical implications for policymakers and patients.
The authors tackled the problem of balancing fairness and efficiency in resource allocation, specifically in kidney exchange, by proposing a hybrid rule that combines lexicographic fairness with a utilitarian objective, and demonstrated its effectiveness on real data with more reliable outcomes than other rules.
Balancing fairness and efficiency in resource allocation is a classical economic and computational problem. The price of fairness measures the worst-case loss of economic efficiency when using an inefficient but fair allocation rule; for indivisible goods in many settings, this price is unacceptably high. One such setting is kidney exchange, where needy patients swap willing but incompatible kidney donors. In this work, we close an open problem regarding the theoretical price of fairness in modern kidney exchanges. We then propose a general hybrid fairness rule that balances a strict lexicographic preference ordering over classes of agents, and a utilitarian objective that maximizes economic efficiency. We develop a utility function for this rule that favors disadvantaged groups lexicographically; but if cost to overall efficiency becomes too high, it switches to a utilitarian objective. This rule has only one parameter which is proportional to a bound on the price of fairness, and can be adjusted by policymakers. We apply this rule to real data from a large kidney exchange and show that our hybrid rule produces more reliable outcomes than other fairness rules.