You run a dating agency. One evening you invite 10 single men and 10 single women to gather. They are each to get one date. The men list the women in order of preference. Man A says he prefers Woman A to Woman B, and Woman B to Woman C, etc. The women rate men in the same way. What’s the best way for you to pair up the men and women?
It’s a tricky problem. So tricky that progress on resolving related problems earned Al Roth a Nobel Prize in economics.
The dating agency exemplifies what economists call a matching market. A matching market is a market in which price is not everything. You can’t buy a date (though it would be difficult to deny that wealth may help you secure one). Still, both sides have to agree to it.
The classic matching market is the labour market. It may be an aspiring journalist’s burning ambition to secure a staff job on the JC, but the paper also has to want you too.
Another matching market, on people’s minds today, is schools and university admissions. Suppose your ideal university is University P, but if you don’t get into University P, you’d prefer University Q to University R, and you’d rather go to University R than University S. The problem with a typical way of allocating university places is that if you aren’t allocated your first choice, you risk failing to secure your second choice too, because that university might fill its places with those who ranked it top. That creates all sorts of difficulties.
Roth’s algorithmic solution is complex, but the kernel is straightforward. To return to the dating agency: imagine your ideal date is widely regarded as the most handsome/beautiful. Unfortunately you are not blessed with Hollywood looks and the person you would most like to date has no interest in dating you. What is needed is a formula to ensure that each person is given their highest ranked date from among the people who are willing to date them. Or, to put it another way, if a man is given a date with Woman Y, but he wishes he were dating Woman X, then he will have been allocated Woman Y only because Woman X does not reciprocate his interest and has been paired off with someone she prefers.
A similar solution to how schools and pupils are matched has been used by Roth to transform the educational landscape across the United States.
Born in New York City in 1951, Roth was raised in New York City, in the borough of Queens (which explains why, he told The JC, he speaks the Queen’s English). Both his parents were high school teachers in New York City’s municipal school system, which he also attended. As a child he went to Hebrew school “for what seemed like many years, in the evenings, until my bar mitzvah.”
In recent years Roth has turned his attention to the kidney “market”. The kidney market is not a market in the conventional sense in that in all countries (bar Iran) you are forbidden to sell your kidney. You may, however, offer one of your healthy kidneys to a loved one. The problem is the match. Your sister may be in need of a kidney, but the kidney you could provide for her would not be a medical fit. So what Roth did was create a non-financial exchange. At its most basic, it operates like this. Suppose my kidney would be compatible for your sister, and your kidney would be compatible for my brother, then, as it were, we swap kidneys — no kidneys are sold, but your sister and my brother both receive the transplants they need.
The kidney exchange he established is still evolving and becoming more sophisticated. But so far it’s helped save the lives of 5,000 people. It’s evidence of the practical impact ideas can have and the ultimate riposte to those who brandish economics “the dismal science”. Roth says that his work in market design is an effort at tikkun olam.
David Edmonds is the host of www.philosophy247.org and www.socialsciencebites.com