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Alvin E. Roth and Lloyd S. Shapley were awarded the Nobel Memorial Prize in Economic Science in mid-October for their work in market design. Shapley and another researcher, David Gale, came up with the Gale-Shapley algorithm, which showed how 10 men and 10 women could be matched so that no two partners would prefer a different partner over their current match.
The Jewish Roth, 60, took this mathematical concept and applied it to the matching of U.S. student doctors to hospitals, a method now used by the National Resident Matching Program. He also used the algorithm to redesign how students apply to New York City public high schools so that fewer students ultimately attend schools that were not among their top choices.
Roth, who also applied his algorithm to the process of kidney organ donation, is currently a visiting professor at Stanford University. He spoke with JNS.org in the following exclusive interview.
How and when did you find out about winning the Nobel Prize, and what was your initial reaction?
We were awakened from sound sleep at around 3:30 in the morning. My wife woke up and said the phone is ringing. She went to our office, brought it back, and it rang again. One of their concerns is that you don’t think it’s a hoax, so he said “I have five or six of my colleagues here, and you know two of them,” and they all can speak to you right now to let you know that it’s the real thing. I talked to a bunch of people in quick succession. It wasn’t unimaginable, (but) when the phone rang at first we thought that a child was in trouble.
What does your market design research entail?
For a long time economists have studied markets as naturally occurring human phenomena. Biologists get to know more about plants so they can do plant readings and try to improve varieties of corn, just as economists like to know more about markets and how they work, and try to make them work a little better, particularly when these run into trouble. Marketplaces are the institutions through which we decide all the things that get allocated, all the scarce resources.
You’re sharing the Nobel Prize with Lloyd S. Shapley. How did you apply his algorithm to matching medical residents with hospitals? What was the main difference between the previous system and what was implemented based on your algorithm?
I knew about Shapley’s work. He was a giant of game theory when I was in graduate school. One of the things that changed was that instead of hospitals proposing to students, we moved it around to students proposing to hospitals, and that allowed us to handle some of complications of the medical market more basically. When the market started, there were no women in American medical schools. Today there are about 50 percent women, and it turns out that a significant number of graduating medical students are married to each other. In recent years there have been about 16,000 graduates of American medical schools, and about 1600 are married to each other. So those two people need two jobs, and they would like to have them both, for instance, in Boston or New York. That gives their preferences a different kind of structure, and they have to be devised a little differently.
How was your algorithm applied in the New York public school system?
New York City has a long history of struggling how to assign children to schools to meet all sorts of rules, as well as solutions to racial segregation chiefly. So New York had a very decentralized public school system partly as a result of that, and when Michael Bloomberg first became mayor, he tried to reassert some municipal control and reform these school systems. What they had before was that each high school sorted its own admissions, and as a result about 17,000 kids a year got multiple offers of which they could only take one. It wasn’t just that they didn’t get into their top choice, but that they were assigned to a place on which they had no information about whether they wanted to go there or not. So now that number is down to about 3,000 from about 30,000.
In the kidney transplant realm, your work has allowed patients to effectively swap incompatible donors with compatible ones from other donor-patient pairs. How does this work?
That’s how the simplest kind of exchange works, a double coincidence of wants, as economists describe it. You have a kidney, we can use it; we have a kidney, you can use it. But often you might have a kidney we can use, but we don’t have a kidney you can use. Maybe someone else has a kidney that you can use. So we started investigating more complicated exchanges, like with three pairs, for example.
In what way did Jewish education and/or upbringing, or religious thought in general, play a role in your life? Have those factors affected your economic research?
In my family we went to a conservative shul. The idea of tikkun olam (repairing the world) is something that fits well with market design because they’re both there to repair the world. There’s a nice story in the Talmud about a Roman woman who asks a rabbi how long did it take Hashem to create the universe, and he says six days, resting on the seventh, and she says to him “What’s he been doing since then?” And the answer is he’s been making matches.
What are you working on these days or planning to work on in the future?
These last two weeks I’ve been answering emails, hundreds a day, and I’m working on a Nobel lecture. Right now I am comfortably busy with the ripples of this award, but I’m teaching a class on market design and a class on experimental economics. One of the very nice things of this Nobel Prize for me is that I’ve gotten it for work that I am still doing right now. There are still valuable things to do, so it’s quite a thrill for me to have work recognized that is what I will go back to as soon as I stop being awarded for it.