Matchmaker, Matchmaker, Find Me a School

Researchers at the University of Michigan and Carnegie Mellon University have analyzed the various student-to-college matching systems utilized in China, which are similar to those developed for Boston and New York’s “school of choice” programs in the United States, and determined that allowing a wider range of choices within each choice band results in more stability, less gaming, and more satisfaction among students with the schools to which they are ultimately matched.

Each year, 10 million high school seniors in China compete for six million seats through a centralized college admissions system, making it the largest centralized matching system in the world. (The nationwide exam takes place June 7-9 in 2017.) This system, similar to that used to match residents to teaching hospitals in the U.S., requires students to submit a prioritized list of their preferred colleges; an algorithm then determines which students are matched to which colleges.

Each of China’s 31 provinces applies its own criteria in determining how students are accepted and each utilizes an independent matching process from one of two classes: sequential or parallel. The sequential mechanism is similar to what Boston used for its public school choice prior to 2005, whereas the parallel mechanism is similar to the new school choice mechanism currently in use in New York City.

The researchers have studied these student-to-college matching mechanisms and determined that the parallel system, now adopted by the majority of Chinese provinces, produces superior results in terms of student satisfaction and stability.

“The matching of students to universities has profound implications for the education and labor markets outcomes for these students,” said Yan Chen, co-author of the study and a professor in the School of Information at the University of Michigan. “The study has applications to educational matching systems elsewhere, such as the school choice programs currently practiced in cities such as Boston and New York.”

In 1952, China instituted the National College Entrance Exam, also known as gaokao, taken by all high school seniors in the country over a three-day period each year.
After receiving their exam scores and learning their ranking, students apply to the universities of their choice. The decision of which universities to include on their list, and in what order, is based on several factors, including the student’s exam score, the prestige of the schools, the student’s degree of risk-aversion, and their perceived likelihood of being accepted.

Until recently, the sequential system, also known as the Boston mechanism (although Boston no longer uses this system in its school choice program), was the only system used to assign students. In that system, a student ranks the schools in order of preference and receives immediate acceptance (or rejection). The disadvantage of the system is that if a student is denied acceptance at his or her top-ranked school, the schools below the first choice may already be filled. As a result, top students frequently chose not to list the very top schools, fearing that they would not be accepted and thus be closed out of any desirable school.

One parent explained the dilemma like this: “My child has been among the best students in his school and school district. He achieved a score of 632 in the college entrance exam last year. Unfortunately, he was not accepted by his first choice. After his first choice rejected him, his second and third choices were already full. My child had no choice but to repeat his senior year.” Repeating the senior year offers students the opportunity to retake the exam and reapply for university acceptance.

The parallel mechanism, or deferred acceptance, is designed to alleviate the problem of high-scoring students not being accepted into any university. With that system, a student submits several “parallel” desirable choices within a band. For example, a student could list three universities in the first band and three more in a second band, in decreasing levels of desirability within each band.

In that method, students gain priority for colleges they have listed in their first band over other students who have listed those colleges in their second band.
“The parallel mechanism is widely perceived to improve the allocation outcomes for students,” Yan Chen said. “People consider it to be fair. It also addresses the problem of a risk-averse student or family not listing their top choice at all, for fear of not getting in and losing out on being accepted at any desirable school.”

To date, 28 of China’s 31 provinces have adopted the parallel mechanism to match students and schools. The researchers found that every newly adopted parallel system was more stable than the immediate acceptance program it replaced. They defined stability as the resulting matching being “envy-free.” That is, there was no unmatched student-school pair, and no situation where a student would rather be assigned to a school where he had a higher priority than at least one student matched to it.

As evidence, when Shanghai switched from the immediate acceptance mechanism in 2007 to a parallel mechanism in 2008, it found a 40 per cent decrease in the number of students who refused to go to the colleges they were matched with.

Since each province can set the number of schools in each band, the researchers also wanted to learn if the number of parallel choices in each band affected manipulation of the system. In other words, if students were listing their choices in bands, in order of priority, were they still using game theory to determine where in their bands to place their preferred schools? “We see that parallel is better than sequential,” Chen said, “but what is the best parallel mechanism?”

The researchers found that the most stable and least manipulable mechanism is employed in Tibet, which allows up to ten choices in the first band. As a result, students are more likely to include their top preferences in their selection and are more likely to be satisfied with the outcome.

“Our study helps policy makers understand the consequences of the number of parallel colleges on the incentives and stability of parallel mechanisms,” Chen said.
“The parallel mechanism allocates students in a fair way and incentivizes truthful ranking. Properly applied, it saves wasted time as students retake their senior year, and avoids wasting scarce university seats, when students refuse to attend the school to which they’re assigned. It has applications for school choice programs in the US and around the world.”

The paper, “Chinese College Admissions and School Choice Reforms: A Theoretical Analysis,” was co-authored by Yan Chen, University of Michigan School of Information, and Onur Kesten, Carnegie Mellon University, and published in the February 2017 issue of the University of Chicago’s Journal of Political Economy.

Posted June 5, 2017