Equity and Efficiency in Dynamic Matching: Extreme Waitlist Policies

Abstract

Waitlists are commonly used to allocate scarce resources such as organs. Waitlist policies
attempt to prioritize agents who wait longer by assigning them priority points (`a la first come
first served). We show that such point systems can lead to severe inequality across the agents’
assignment probabilities, unless they use randomization. In particular, deterministic point sys-
tems lead to a more unequal allocation than any other rule that prioritizes earlier arrivals, an
axiom that ensures that agents who wait longer are treated (weakly) better. Among the policies
abiding by this axiom, we show that service in random order (SIRO) leads to the most equal
allocation.

From a utilitarian perspective, we show that the planner faces no tradeoff between equity
and efficiency when the flow utility from waiting is nonnegative, or negative and increasing
over time. In these cases, SIRO is also the most efficient policy. However, when the flow cost
of waiting increases over time, then the planner may face an efficiency-equity tradeoff: SIRO
remains the most equitable policy but may not be the most efficient one.