New York City’s high school admissions process is known for being complicated. But before its overhaul in 2003, the system was dysfunctional in big ways: it left about one in three ninth-graders-to-be without a school assignment until just before the year started, encouraged principals to admit students through back channels, and forced savvy students to develop complicated strategies for getting into desirable schools. Economist Alvin Roth, who won the 2012 Nobel Prize in economics for his work in market design, was part of the team that developed today’s system, which uses a “deferred acceptance algorithm” to match students and schools based on their highest mutual preference. In his new book, Roth offers an economist’s answer to an important question: Why do some eighth graders still not get into any high schools of their choice?

School choice operates under a lot of constraints, and many people have to sign off on any innovations. Sometimes this led to unavoidable complications. Not all of these complications were unavoidable, but just as in kidney exchange, my economist colleagues and I were only advisers, and not all of our advice was adopted. (This is pretty typical of market design, by the way.)

So, for example, in practice the deferred acceptance algorithm is actually run more than once. That’s because there are several specialized schools that form their preferences strictly on the basis of exam scores or auditions. By tradition, students offered a place in these schools must also be offered a place in one of the regular high schools. Thus members of this small group of students each receive two offers of admission even before the main round of the match is run. Their offers are determined by running the full deferred acceptance algorithm on all students’ submitted preferences and then running it again for all the other students after these select students have been placed.

Another simplification I made in my description is that students can list as many schools as they like. We economists recommended that students be allowed to do just that, but on this important detail we did not prevail. So New York City students today can list only up to twelve programs among the hundreds that the city offers. Students who want to list more than that face a strategic choice of which twelve to list. But they still should list those twelve in order of their true preferences. That’s perfectly safe; they can’t do any better.

A more serious problem is that some students list too few choices to get matched. Each year the New York media report on students who listed only schools that require scores higher than they have. These students end up without school placements at the end of the main match. For them, there is a supplemental round, in which they submit a new rank order list of up to twelve schools from among those that still have seats. By that time, the most-sought-after schools have already been filled.

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In 2011, after the main round of the match was announced, I received an email from “Jimmy,” who said he was a thirteen-year-old student from Queens. He appealed for help because he’d been rejected by the five schools that he’d listed in the main match, despite solid grades. He told me that he dreamed of attending Harvard and was worried that he’d be choosing, in the supplemental match, among less desirable high schools that would limit his prospects. I couldn’t help much — my colleagues and I may have designed the algorithm, but we have no role in its annual operation. But I did inquire of a former administrator about what might have gone wrong.

He immediately focused on Jimmy’s math grade of 85 and said that none of the five schools that Jimmy had listed were likely to accept a student whose grade wasn’t at least 90. Jimmy hadn’t received good advice before he compiled his list.

I advised Jimmy to immediately talk to his middle school guidance counselor about how to approach the supplemental round. I ended with a little advice for when he applied to college — something I wished I could’ve have told him before he filled out his high school list: “Bear in mind that admission to Harvard and other top universities is very competitive, so be sure to apply to other schools, including some safe schools.” Almost no one who lists twelve schools is left unmatched in the main round of the New York high school match. So if you know someone like Jimmy, encourage him or her to submit a long list of schools, just to be safe.

These small problems don’t overshadow the benefits the new system brought to New York high schoolers. In the first year of operation, the number of students left to be matched to a school for which they hadn’t indicated a preference was 3,000, down from 30,000 the previous year. A more surprising (and equally satisfying) development was that in each of the first three years of operation, the number of students who got their first choice increased, as did those who got their second through fifth choices.

“It worked even better than we expected in terms of kids getting their top choices,” Jeremy Lack says. “It really empowered the students.”

We weren’t surprised that the new system would immediately work better than the old one, but we’d made no changes in the algorithm in years two or three, so why did the system continue to improve?

Remember those seats that principals would withhold? It appears that principals were gaining confidence in the new system and understanding that they’d actually prefer students assigned by the algorithm to those they could admit later. As a result, more and more of them released all of their saved seats to the central match. It was as if, by creating a stable matching each year so that principals would be eager to enroll students through the centralized process, the Department of Education was creating thousands more places in desirable schools.

One reason that principals gained confidence was that DOE staffers did a good job communicating to them how the new system would work. Crucial in that effort was Neil Dorosin, the DOE’s director of high school operations. The task of informing everyone about the new algorithm fell to Neil and his colleagues in the Office of Enrollment Services. Among those he had to educate was his ultimate boss, Chancellor Joel Klein.

“One day I got called down to talk to him,” Neil recalls. “He was upset because he had a friend whose child didn’t get into their first-choice school. The friend had a cousin whose child had gotten into the school, and it was their last choice. I had to explain why the system had to function that way” (i.e., to make it safe to list true preferences).

More than ten years later, New York’s high school choice system is holding up well. The clearinghouse we designed is just a part of the sometimes forbidding gauntlet that families have to run to inform themselves about schools and decide how to rank them. But with the exception of some of the complications I mentioned, once families are informed, the school choice system no longer presents them with complicated strategic problems. Most important, it’s no longer a congested process that leaves tens of thousands of students to be placed at the last minute into schools for which they’ve expressed no preference.

Excerpted from WHO GETS WHAT – AND WHY: The New Economics of Matchmaking and Market Design by Alvin E. Roth. Copyright © 2015 by Alvin E. Roth. Used by permission of Eamon Dolan Books / Houghton Mifflin Harcourt Publishing Company. All rights reserved.