Target the Vulnerable? An Analysis of Rapid Rehousing Prioritization

We model the problem facing a policymaker who must allocate rapid rehousing support to people experiencing homelessness and wishes to minimize the steady-state social cost of homelessness. Support is often given to the most vulnerable applicants or to applicants most likely to remain housed. Although these approaches can be effective in some cases, in general, they may result in a homeless population that is arbitrarily larger than what could be achieved by an optimal policy. We propose an alternative priority queue that is approximately optimal. We then study a family of policies where the policymaker does not differentiate between agents based on their characteristics. Within this family, first-in, first-out (FIFO) queues best target the most vulnerable. If the most vulnerable households benefit most from housing assistance, then an FIFO queue minimizes the expected unhoused population. Conversely, a last-in, first-out queue is optimal if the least vulnerable households benefit most from housing assistance. Finally, we expand our model to allow households to choose among several allocation systems. We show that even in this larger family of policies, if the most vulnerable households are also the ones that most benefit from housing assistance, an FIFO queue minimizes the expected unhoused population. History: This paper has been accepted for the Mathematics of Operations Research Special Issue on Market Design. Funding: This work was supported by the National Science Foundation CAREER AWARD [Grant 2339912; CAREER: Efficient and Equitable Housing Allocation (University of Minnesota, Twin Cities)].