How to find a perfect match for a Nobel

20th October, 2012

‘The Nobel Prize for economics has been awarded to Americans Alvin Roth and Lloyd Shapley for their independent work into how best to bring different parties together for mutual benefit.’

Financial Times, October 16

It’s not really a Nobel Prize, is it?

I’m glad you’ve mentioned that because it’s an important point that is rarely made – except, of course, any time anybody says or types the words “Nobel Prize for economics”, at which point a spontaneous chorus of “there is no Nobel Prize for economics” will break out. No, it is more recent than the original Nobel Prizes, and has a lengthy name. It undoubtedly does not deserve the status of, for instance, the Nobel Prize for literature (never awarded to Leo Tolstoy or James Joyce) or the Nobel Prize for peace (awarded to Henry Kissinger, the EU and most controversially to the Cabbage Patch Kids).

You seem touchy.

Perhaps a bit, yes.

Apparently this week it was awarded to Alvin Roth and some other guy.

I feel a little sorry for Lloyd Shapley, and not just because he should have been awarded the prize back in 1994. He has been somewhat eclipsed by Prof Roth, and this does happen. In 2005, the prize was awarded to Thomas Schelling, a brilliant writer who analysed everything from quitting smoking to winning the cold war, and Robert Aumann, who did something so abstruse and mathematical that nobody knew what it was. Not surprisingly everybody talked about Prof Schelling. It’s similar here: Prof Roth seems an intensely practical economist, charging around writing papers about dwarf-tossing and setting up life-saving kidney transplant operations, while all Prof Shapley produced was some mouldy old maths.

I thought he ran a dating agency, or something?

With the late David Gale, he designed a matching algorithm and used marriage as an example.

You economists are such romantics. You’re making me blush.

The algorithm was not actually designed to arrange marriages. It was to analyse ways to match things up. Imagine a world where husbands and wives were pair up by some automatic, algorithmic process.

They aren’t.

No, but schools and schoolchildren are, for example, as are teaching hospitals and medical students. Prof Shapley and Gale discovered a simple rule that would allow these matches to be made. After the algorithm had done its work, no two people would have an incentive to peel off and do some kind of side deal together, which is important if the algorithm is supposed to function in a free society.

How does the algorithm work?

One simple variant is for each of the men to propose marriage to one of the women. The women must reject all but one, and hold on to the best one temporarily. Each rejected man gets to make a second offer, and again the women get to hold on to the offer they had before, or alternatively reject it and hold a different offer. The point at which no man is rejected is the point at which you can close the market and tie the knot. And the allocation will be stable.

It seems rather traditional. Can’t the women propose instead?

Sure. If they do, it turns out that you will get a different but still stable set of matches, and this set will be one that the women prefer. So this was the theory, and Prof Roth developed the theory and put it into practice.

And it was Prof Roth who set up the dating agency?

He patched up the way in which medical students were matched with their first hospital jobs, which is more complex because some students are couples and want to apply for pairs of jobs in the same city. When Prof Roth looked at the problem, in the mid-1990s, the matching procedure being used was unstable. Offers – or ultimatums – were handed out many months in advance because people preferred their side deals to the centralised system. This is a classic symptom of unstable matches. He fixed it.

And got a Nobel Prize for that?

Yes, along with designing algorithms to match students with schools and kidney donors with recipients. And he deserves it. Prof Roth does three things that are far too rare in economics. First, he really engages with the anthropological reality of how individual markets work, rather than immediately leaping to an abstract model. Second, he recognises ethical or cultural constraints – we don’t like the idea of buying and selling kidneys, for instance. Too many economists have simply argued that the constraints make no sense, shrugged and walked away. Prof Roth accepted them as a fact of life and worked around them.

He’s almost human.

Indeed. And an important point is that many of the markets Prof Roth has designed do not and cannot work perfectly. A lot of theoretical economics is concerned with proving that perfection is possible, or impossible. Prof Roth is interested in answering the pragmatic question “is this good enough?”.

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