They may not know it, but every year millions of K–12 children in cities across the U.S. are being matched with top public schools outside of their neighborhoods by computer algorithms. What’s more, many of these matching systems, dependent on a number of variables, are subject to manipulation and fraught with inequity.
In an effort to circumvent that inequity, a few cities, including Boston and New York, have adopted algorithms that are less prone to tweaking — producing a higher percentage of favorable outcomes, or top school picks, for students than in the past. Other cities, meanwhile, still use manipulable matching models, such as the Boston Mechanism, which are inherently problematic. For instance, if a school is very popular, a student, figuring she doesn’t have a shot at a spot there, strategically lists her second-choice school as her top pick. (Students who rank a school highly have priority above those who don’t.) She knows that if she lists the popular school as her first choice and doesn’t get it, she’ll have jeopardized her chance at her second, and maybe even third, choice, since all those seats will get doled out to students who list those schools as their first choice.
It’s a process — initially designed to give disadvantaged children a chance to attend better schools beyond their neighborhood — that’s beset by challenges. Many students are unsure how to strategize in ranking their choices, while others might not even know they should be making strategic decisions. What’s worse: The kids who list their picks naively or truthfully could be taking a back seat to those who know how to game the system.
Private School Boost
Recent research by Mohammad Akbarpour, an assistant professor of economics at Stanford Graduate School of Business, and Winnie van Dijk, a research fellow at the Becker Friedman Institute for Economics at the University of Chicago, reveals another discrepancy that’s undermining the system. Designers of school choice systems typically have failed to consider that some students have access to private schools and some don’t. This oversight, says Akbarpour, can lead to circumstances in which lotteries for public school seats unintentionally favor students with access to private schools. This means a student fortunate enough to have an attractive outside option — in this case, a private school — is better positioned in the public school system than a child without the means to attend a private school. Knowing they’ve got a private school as plan B, they can shoot for their top-choice public school, while others are left to strategically target their second-, third-, or fourth-choice school.
“Any economic model that you write has a lot of assumptions and they have consequences — people forget to question the assumptions to begin with,” says Akbarpour. “For a lot of school choice mechanisms where your best strategy is not to report truthfully, and your options include a good outside one, you can always risk and go for the best public school. You have to strategize less — that makes you better off.”
Akbarpour’s study of school choice systems fits into a larger agenda that drives much of his work: how to design markets in ways that improve the distribution of wealth, whether that’s access to the best public schools, price controls on hand sanitizer during the COVID-19 crisis, or the ability to find kidney donors. To study school choice mechanisms, Akbarpour partnered with van Dijk, who had been looking into the allocation of public housing in Amsterdam. She was interested in understanding whether residents with outside options — such as being able to wait out long queues by moving in with parents or making other arrangements — were more likely to secure the best living quarters in the city’s public housing system.
“Designers of school choice systems often assume that everyone who participates in the matching prefers ranking all schools over being unassigned. Winnie came to my office with this idea about the role of outside options in matching markets, and we started thinking about outside options in school choice and how their presence changes the way that a school choice system allocates seats,” said Akbarpour.
Increasing Diversity of Students
One of their key findings was that in a district that uses a mechanism open to manipulation, kids without a private school option are more likely to report their top picks untruthfully — they list their second or third choice first, figuring the school they really want to attend, if it’s popular, will be filled. The result is a higher likelihood that affluent students will land a seat at the popular school while students without an outside option are left to compete for lesser-choice schools — further reducing the competition among better-off students vying for the best public school seats.
For school districts looking to increase the diversity of students at their best schools, these findings bolster the argument for implementing strategy-proof mechanisms like deferred acceptance — the process by which the majority of fifth graders in New York City apply for middle school. Here’s how it works: Students list their favorite schools in order of preference. Schools reject the lowest-ranking students in excess of their capacity, and the rest are held temporarily until the algorithm finishes and no more matches are made. If a student is rejected by their first choice, they go through the same process with their second and possibly third choice. Schools consider the deferred students (those being held) and allot seats in priority order based on their own set of variables outside the algorithm — such as test scores or siblings already in attendance. The upshot: Kids who don’t get matched with their top choice still have a good chance at getting their second or third choice — removing the incentive to list preferences strategically or dishonestly.
While strategy-proof mechanisms like deferred acceptance aren’t flawless (many New York schools also consider a variety of potentially manipulable factors like test scores, attendance records, and conduct history), they have resulted in a higher percentage of favorable matches than in the past, when the methods in place regularly led to higher-performing students receiving multiple matches while lower-performing students collected none.
Designing other strategy-proof methods, which makes it safe for all students to report their choices honestly, is a crucial step toward leveling the playing field in many applications. Says Akbarpour, “What we’re doing here is another argument for why truthful mechanisms are good.”