Waiting lists can be used to allocate scarce goods, be they hard-to-get preschool slots or organs needed for transplants. But poorly designed lists can be inefficient and unfair, finds Chicago Booth’s Jacob Leshno, who suggests a better version.
To study this issue, Leshno looked at the system used to assign subsidized housing in the United States. Americans who qualify for subsidized apartments can put their name on a first-come-first-serve list with housing authorities. Once an applicant’s name is called, she can accept or reject the offered apartment. If she rejects it, her name might drop to the bottom of the list.
The amount of time an applicant waits for an apartment is random. Someone who puts his name in at an inopportune time may face a long wait. Moreover, if that wait time stretches into years, the applicant might accept an apartment other than the one he really needs, simply to cut the wait time. He may feel forced to accept an apartment that’s far from work, school, or family.
And a long commute can have consequences for a family, and others. Children who travel far to attend school suffer, and they may run into social difficulties if required to switch schools because their families have to move. Relocating can break community bonds. In short, this system can cause people to make decisions that hurt themselves and society.
Leshno used a dynamic model to determine how fluctuations in the length of time people expect to wait in line affect their welfare. Considering other systems, he lands on a “service in random order” queuing mechanism, in the parlance of queuing theory. This would let applicants choose an apartment complex they prefer, and then would place them in a pooled list for vacancies there. In this system, when an apartment at a given complex becomes available, the housing authority chooses one applicant at random from the pooled list for that complex, and the applicant then accepts or rejects the offer. If they reject it, they remain on the complex’s pooled list.
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Amy R. Ward Says Customers Are Getting ImpatientApplicants are not necessarily offered apartments in the order that they apply, which may seem unfair to some. But does fairness dictate that applicants should be offered apartments in the same order in which they signed the waiting list? Leshno cites day-care lists as an example to the contrary. “Local parents may be able to register for daycare centers years in advance, whereas advanced registration is not possible for recently moved parents who may have a greater need for daycare.”
Leshno says his suggested queue is more efficient because applicants are offered more similar opportunities. In the current system, people can be on a housing list for days, months, or even years, and two families vying for the same type of apartment might face very different wait times. But Leshno says to focus on the expected wait time at the point in time a person is called. At that point, in his version, the expected wait time is likely to be more stable over time and give every applicant, regardless of when they’re called, similar apartment options.
Jacob Leshno, “Dynamic Matching in Overloaded Waiting-Lists,” Working paper, August 2019.
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