Two Americans were awarded the Nobel Prize in economics yesterday, and their work has already been put to use at several of the nation’s largest school districts.
Lloyd S. Shapley came up with the idea of figuring out how to create perfect matches even when the two parties don’t necessarily agree on what makes an ideal match. He was thinking of finding a way to create perfect marriages. But it was the other winner, Alvin E. Roth, who put that idea to use.
Roth used Shapley’s formula to come up with an algorithm that matches schools and students in public districts. New York, Boston, Chicago and Denver schools all use Roth’s method.
The problem with school matching was that students were told to list their top school choices, and then ended up not going to any of those schools. That’s because their top pick was usually a pretty popular choice, meaning lots of competition and a slim chance of getting in. Same with options two and three.
Eventually, some families figured they’d submit their second choice as their top pick, figuring that way they’d have a chance of at least getting into one of their preferred schools. But, that meant bumping other folks off the list who actually did want to go to that second-choice school.
That is the problem that Roth tackled, and the New York Times explains how he went about it:
Mr. Roth designed a system in which students had an incentive to tell the truth about where they wanted to go. A centralized office could then assign them to a school best suited for them, based both on their own preferences and the preferences of the schools they were applying to.
The school systems he helped create use a “deferred acceptance algorithm,” which was developed by Mr. Shapley’s theoretical work.
The system works by tentatively accepting students to their top-choice school. It holds off on the final assignment until it has gone through all the other applications to make sure there are not other students who have a higher claim to a spot at that given school (because of higher test scores, a sibling at the school or whatever other criteria the school prioritizes), even if those students happened to rank the school lower on their list of preferences.
Jerry Burrell, director of enrollment planning and support for the Boston public schools, said Roth’s assignment model, implemented in the 2006-2007 school year, was “a leap forward” for parents and students.
“Now, they can just pick the school that they really want, without worrying that they will be penalized,” he said.
Meanwhile San Francisco Public Schools considered implementing Roth’s system a few years ago, but ultimately decided not to. From the San Francisco Chronicle:
In March 2010, the San Francisco Board of Education adopted an “assignment with transfers” plan Roth and his colleagues developed but were later told by district staff, according to Roth, “that they decided to do further development in-house, and so will develop software to implement the new design on their own.”
A new application process, put in place beginning in the 2012 academic year, does appear to take ranked choice more into account, and in March the district posted an explainer about the “student assignment computer program” on its website ( sfg.ly/RzayTM). But, Roth said, it has provided limited information on how the algorithms actually work.
Roth’s work has also been used to improve the matching system for medical school graduates when they do their residency at a hospital, and to improve matching for transplant programs.