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. In this work, we propose a 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 that favors disadvantaged groups lexicographically; but if cost to overall efficiency becomes too high, it smoothly 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 kidney exchange, where needy patients swap willing but incompatible donors, and demonstrate on real data from a large exchange that our hybrid rule produces more reliable outcomes than other fairness rules.
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