Evening the Odds

ISyE Assistant Professor Nick Arnosti sees single lottery systems as a tool for good that could improve the lives of students and people living in public housing.

In the United States, more than 10 million people rely on federal rental assistance for their housing, according to the Center on Budget and Policy Priorities. Nearly 70 percent of these Americans are seniors, children, or people with disabilities who would otherwise be homeless if it weren’t for public agencies overseeing the allocation of affordable housing. However, the demand for affordable housing in America far outstrips supply. In an effort to fairly distribute the limited apartments and homes, public agencies in cities across the country have turned to lotteries and wait-lists.

“Every lottery and wait-list has slightly different rules about who’s eligible, how you apply, and how the lottery is run,” says ISyE Assistant Professor Nick Arnosti. “No two systems are alike; there really are a million variations. But rather than getting lost in the details, I think the important question to ask is: Are we giving people choice?”

For years, Arnosti has been studying housing allocation systems in the United States, particularly in New York City, to understand which types of lotteries or wait-lists generate better outcomes for more people. His interest began in 2016, the year he moved to New York City for an assistant professorship position at Columbia University. Witnessing how deeply the issue impacted so many people led Arnosti to partner with Peng Shi, an assistant professor at the University of Southern California.

Arnosti and Shi discovered there was no perfect, one-size-fits-all lottery or wait-list system for cities to adopt. “Instead, cities implementing their own allocation systems need to watch out for implicitly penalizing applicants for being selective, as selectivity in housing allocation is a good thing and leads to a higher quality of matches,” says Shi.

Generally, people who qualify for affordable housing are given options based on their need. Need is determined by one’s income and job, among other factors. Agencies attempt to give priority to those with the greatest need, which is known as targeting. Arnosti and Shi believe that more attention should be paid to a second objective: matching applicants to their ideal residence.

“It’s extremely rare for applicants to be asked about their preferences,” says Arnosti. Currently, agencies consider family size, preventing a family of four from landing in a one-bedroom apartment. Yet, Arnosti believes much more should be taken into account. “It is uncommon for applicants to have the chance to say where they’d like to live,” he says, “and that’s where I think there could be a lot of gains. One way to do that would be to show candidates in advance some housing options that might become available within the next six months, and then ask: Which ones look interesting?”

Although public housing agencies have historically emphasized targeting, Edward Kaplan believes Arnosti and Shi’s research has breathed new life into the debate over the value of matching. “The tradeoff between matching and targeting is really interesting and important,” says Kaplan, who studies public housing allocation as a professor of engineering at Yale University. “Trying to get better matching results could contribute meaningfully to individuals’ feelings of security, along with other aspects of preference. Arnosti and Shi’s work suggests [new] ways to think about paying more attention to the matching aspects of the problem.”

In the quest for fairness, Kaplan has found academics tend to favor lotteries over wait-lists. “They are easy to implement and often have built-in fairness properties,” says Kaplan. However, Arnosti and Shi are interested in finding ways to improve both systems.

For example, outside of the United States, wait-lists for public housing look much different. Arnosti points to Amsterdam as a potential model for local agencies to follow. There, roughly 40 percent of the population relies on public housing, and residents keep their position in the waitlist until matched to an apartment they find suitable. “But in St. Paul, for example, it’s a take-it-or-leave-it offer,” says Arnosti. “If you say no, you lose your spot on the list.” When applicants have to wait many years for their next offer, most will accept the first offer they receive, even if it isn’t a great match.

For cities that allocate housing using lotteries, rather than wait-lists, Arnosti and Shi argue that using a single priority list for many buildings would give people more choice.  “Right now, most lottery systems are done independently for each new building,” says Arnosti. “As a result, most people will win at most one lottery, and therefore not have much choice. Using a single lottery that applies to many or all buildings enhances choice: There will still be losers, but this way, the winners are allowed to choose among many buildings.”

“I think the important question to ask is: Are we giving people choice?”

—Nick Arnosti, ISyE Assistant Professor

Additionally, Shi suggests increased collaboration between academics and policymakers as a solution. As it stands today, “it may be too much to ask for policymakers to understand all the nuances of the [lottery] design details,” says Shi.

However housing is allocated, Arnosti believes the power of choice has the greatest chance to improve outcomes and people’s lives. “There are tradeoffs involved in the choice between a lottery and a wait-list, but either system can work well,” says Arnosti. “My goal is to identify opportunities for win-win changes that offer people more say in where they’re going to live.”


Rolling the dice on school choice

Many schools have long been experimenting with lotteries. As teenagers finish junior high and enter high school—or if they simply wish to switch schools—certain education systems are designing their own lottery process to determine student admission. Much like public housing allocation, many different systems are in use.

Arnosti spent years studying New York City schools and their experience running separate lotteries for each school, also known as independent lotteries. When applying, students are encouraged to rank up to 12 schools they like, leaving them with a choice between the ones where they were admitted. While this may sound fair on paper, Arnosti says, “you’re actually screwing some unfortunate people who draw bad lottery numbers at every single school at the same time.”

It turned out independent lotteries weren’t generating the best outcomes for the largest number of students. Due to the randomness in lotteries, students who ranked a school fourth or fifth on their list were oftentimes admitted over other students who ranked the same school first on their list. Meanwhile, swapping schools with another student so both received their first choices was not allowed. These unsatisfying outcomes prompted school administrators in New York City to reevaluate. Using student preferences, they simulated multiple lottery models to see how they could improve results for their entire student population.

“In the end, they realized they were getting a better match—basically more students getting their top choices—when they used a single lottery,” says Arnosti, “even though that wouldn’t necessarily be your first instinct.”

Unlike independent lotteries, single-lottery systems combine all of the schools in an area or district into one lottery. As with affordable housing, this ensures that people with good lottery numbers have many options to choose from. “It’s a simple solution and it works pretty well,” says Arnosti. “But there are consequences to a single lottery system. My work shows that using a single lottery often results in more students being administratively assigned to some school they didn’t list. This finding provides administrators with more information about how lottery design affects the final outcome.”

Of course, admissions are not solely determined by lottery. Schools often prioritize siblings of current students, or children who live nearby. They also may grant priority to students with special needs. Arnosti says that school choice algorithms help ensure that priorities are stated transparently and applied consistently.

“At the end of the day, however, there is no perfect system: So long as there is a shortage of high-quality schools and affordable housing, some people will be left with bad options,” says Arnosti. “But some systems are better than others. The worst thing you can do with something that has high demand and limited supply is to give it to someone who doesn’t really value it and would have much preferred something else.”