How (Not) to Allocate Affordable Housing
AbstractWe study a setting in which items are dynamically assigned to waiting agents. The common practice of using independent lotteries encourages agents to enter many lotteries, resulting in inefficient matching. We consider several alternatives, and reach three main conclusions.
First, systems with very different descriptions can produce identical outcomes. In particular, Independent lotteries are equivalent to a waitlist in which participants lose their position if they reject an offer; Restricting agents to enter at most one lottery is equivalent to using a waitlist in which participants keep their position after rejecting an offer, and both are equivalent to using artificial currency.
Second, when an agent’s level of need is unobservable, there is often a tradeoff between matching (assigning agents to items that are a good fit) and targeting (assigning items to agents with the greatest need).
Third, it is generally preferable to prioritize good matching over effective targeting. The exception is when most participants have very little need, and the remainder are far more desperate. In such circumstances,effective targeting can be achieved by adding friction to the assignment system.
Our findings suggest that independent lotteries are rarely advisable. We discuss the implications of our work for the allocation of affordable housing, and of discounted tickets to Broadway shows.