abstract
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.