Alvin Roth Receives Economics Nobel For Flawed Residency Match System

There’s a larger question here about why the scholarly world allows itself to be judged by secretive Scandinavian committees sitting on endowments funded by money made selling explosives. But let’s put anti-Nobel polemics aside.

The announcement today that Alvin Roth and Lloyd Shapley won this year’s award in economics came with the explanation that they had devised systems for matching buyers and sellers that led to more rational outcomes than existing markets.

Shapley, a contemporary of “A Beautiful Mind’s” John Nash, introduced an elegant theory 50 years ago to explain the (relative) stability of marriage pairings despite the fact that individuals have complicated preferences when choosing a mate. Shapley’s idea is that the person you end up with is the best match given everyone else’s preferences.

You might prefer someone else more than your current mate, but that person has you lower on her list, and so on. Imagine Larry. If he could Larry would have definitely married Elizabeth Taylor. But she was taken so now Larry is happy with his actual wife. (To sum it up in a way that would make an economist cringe.)

Alvin Roth built on that early theory. He designed actual markets that used the matching principle, also known as the deferred acceptance algorithm, as a guiding principle. The most famous example of a Roth market is the Residency Match.

Medical residency is a job that lasts three to seven years, depending on the program, and follows graduation from medical school. It is required for a doctor to complete a residency in order to be licensed to practice.

In the “old days” medical students would apply to hospitals and rank their preferences in a way that was visible to those institutions. A hospital would first review those applicants who had indicated them as the first choice. If spots remained to fill, a hospital would then look at those who had picked it second, and so on. You can quickly see how this system punished people who shot high and missed. They would end up at one of their last choices because the best places would fill up quickly.

Roth’s clever solution was to gather everyone’s preferences at once. By receiving match lists from doctors and hospitals at the same time, a computer could take the entire applicant pool’s preferences into consideration.

In practice this means that if Doctor Jones ranks University Hospital first and it ranks Jones first as well, they will match. If Jones ranks University Hospital third, but her top two choices fill their spots with other applicants whom they prefer over her, she still matches at University Hospital. University Hospital will never know it was Dr. Jones’ third choice. The system works well at what it does, which is to create a simultaneous match of thousands of people at once that is less subject to gaming than the old method.

Why then, do so few physicians embrace the match? (And why do so many actively despise it?)

The answer may be that if you look at every other elite professional training paths, whether law schools, business, PhD programs in the arts and sciences, architecture, you name it–there are no other matches. No other fields except medicine have concluded that this kind of system is a rational way to match applicants and schools or job-seekers and jobs.

A match is certainly an efficient way for hospitals put together a residency class. And going through the hyper-rational process fits in well with other cultural artifacts of medicine like memorizing a thousand carbon molecules to pass organic chemistry or spending six months studying for the MCATs.

But it’s not a good system, despite what the Swedes may think.

For one thing, the match is tremendously family-unfriendly. Consider this scenario. There are two couples. In each couple both are pursuing professional careers. In the first couple, the husband is a medical student and will soon go through the match. In the second couple, the husband has an entry level finance job and will soon apply to business schools.

Without meaning to rehash Lloyd Shapley’s original point about marriage, which wife would you rather be?

You have your own career to attend to and you need to plan for the future. If you married the med student, a computer will tell you where you are moving the following year. Usually there is a delay of six months to a year and a half between “match day” and the start of residency. If you don’t like what the computer spits out, tough luck and try again in your next lifetime. Or get divorced. There’s always that option.

If you married the finance guy your husband will be applying to several business schools, weighing offers and giving you time to think about where you might work if a move is required. Maybe he does not like his options and decides to reapply or skip B-school altogether.

Which scenario is friendlier to two-career households?

The match allows organized medicine to continue to live in a world where a physician gets told where to go, his family be damned. That’s a major dissatisfier among physicians I know. I have a friend who opened his envelope and was told he would be moving 1,000 miles away from everyone he knew because he got his ninth choice. He’s still not sure why or how that happened inside the black box of the match day computer.

I’m not doubting that the preferences worked out that way, but these same medical students would have behaved differently, maybe applying in a different specialty if they had been working in a system that was less abrupt, less hyper-rational, and more forgiving of ambiguity (like most markets tend to be).

Another reason that the Residency Match drives doctors nuts is how impersonal it is. Who else likes to be reduced to a name on a list?

Using marriage again as an example, is this how chemistry works in the real world? If it were so, we’d all show up at big stadiums and conduct massive speed-dating exercises. We’d submit rank lists. At the end of the weekend a computer would tell us whom we are marrying. I’m only sort of joking.

The match process does not allow for a residency program to recruit someone who might not otherwise rank it highly. (A wife you might not find attractive initially, but whose winning personality carries the day…)

The match process does not allow the director of a residency program to build a residency program that’s multifaceted. You can’t say I want three doctors who excel at bedside manner and three more who are analytically off the charts. Instead you rank and pray.

The argument here is not that Alvin Roth is undeserving of the award, or that his inventions and ideas are not interesting or impressive. But it is ironic that the most famous real-world manifestation of his ideas is, at least within the field, a disaster.

Giving the Nobel to the Residency Match reminds me of another Nobel Prize in economics. Remember when the options-pricing pioneer Robert Merton won the award in 1997 a year before his hedge fund Long Term Capital Management imploded and almost took down the world financial system?

Maybe those examples say more about the field of economics than anything else. Theory beats practice, at least for the Scandinavian bankers who decide.

David Whelan is a contributing editor at Forbes, where he was a staff writer for 8 years covering health care payers, providers and policy. He’s currently studying and working in hospital administration. Follow him on Twitter @WhelanHealth. This post first appeared on Forbes.

3 replies »

  1. Your analysis is flawed. Your facts are imagined. No wonder you’re in hospital administration.

    The match system is very popular and has excellent satisfaction rate. You don’t understand it. Please don’t complain.

    The medical student who had to move 1000 miles away for residency would not have matched anywhere under the new or old system if he didn’t rank a place 1,000 miles away or would have matched at a less prestigious institution, depending on his particular merits. Neither of those options were acceptable to him as he could have not ranked the place 1,000 miles away or could have ranked a less prestigious places closer to home higher up and matched there.

    Similarly qualified business school applicant who wants to be in the top 10 schools (similarly competitive as the least competitive medschool) would not have a choice and would have to move 1,000 miles if he wants to go to a top 10 business school or else settle for a 3rd tier local business school that will lead to unemployment in this economy. Of course, business schools are a dime a dozen and you can easily get into one within 50 miles of any major population center.

  2. Not to be too glib, but saying that something is “flawed” is about as important as saying it exists in the real world.

    You want it to be a market system? What do you suggest – students pay to reserve spots? Or maybe the “price” we would pay is accepting residency spots far before we’re ready to make a decision. The whole genius of Roth’s work is the market has no price mechanism to coordinate around so this is what’s left.

    You don’t like something… but I don’t see a better solution offered here. And from what I’ve read about the system in the past, we didn’t have one before either.

    P.S. I will be applying to residencies in one year. I am well aware that there are lots of aspects of the match I don’t like. But perhaps my biggest complaint is that the average medical student applies to 30-40 programs. This overemphasis on playing it safe means more residencies have to say “no” and more students ignore their true preferences when listing where they would be willing to go.