How (Not) to Allocate Affordable Housing

Abstract

We consider a setting in which agents and items match dynamically over time. We show that repeated independent lotteries with unlimited entry (which are commonly used in practice) encourage agents to enter many lotteries, and may result in low match value. We consider three alternate mechanisms: allowing agents to save unused tickets, limiting agents to entering at most one lottery, and allocating developments using a waiting list. We show that these three mechanisms are equivalent: for each agent, the probability of matching and expected value conditioned on matching are identical. Compared to a repeated lottery, these mechanisms result in higher-quality matches for matched agents. However, in some cases, a repeated lottery is more likely to match agents with the worst outside options, and thus may outperform the other mechanisms in terms of utilitarian welfare. We discuss the implications of these findings for two systems in New York City that currently use a repeated lottery: the allocation of affordable housing and of discounted tickets to broadway shows.