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Matchmaking

Think Wedding Woes, Win a Nobel Prize

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A study of marriage biases yields a way to reverse lopsided power equations in other markets

As a discipline, economics was dismal enough before it ventured into matrimony, as David Gale and Lloyd Shapley dared do in 1962. Now that the latter, a UCLA professor, has won 2012’s Nobel Prize for Economics alongwith Alvin Roth, a Harvard Business School professor currently at Stanford, their theories bear a brainy stamp of usefulness. Not in arranging marriages, for which nothing can be useful, but in the theoretical field of ‘market design’, which finds wide application in setting up other kinds of markets designed to yield optimal matches between one class of ‘agents’ and another without prices playing any role. As the Nobel citation reads, Shapley and Roth have been awarded this year’s prize ‘for the theory of stable allocations and the practice of market design’.

In most markets, prices are hailed as heroic. They serve as a mechanism to achieve stability. It’s basic economics. If market supply is short, buyers vie with one another for the product, bidding its price up till such a point that demand declines (as it goes beyond the reach of more and more); its price re-settles where supply and demand attain a new balance. A price spike, though, also acts as a ‘signal’ of potential profit to producers, who rush to raise output… and so the price slides back. If the market is oversupplied, it works the other way round. Either way, it is prices that match buyers and sellers (‘agents’ as economists call them).

Ah, but as Oscar Wilde put it, a cynic is someone who knows the price of everything and value of nothing. And value, even economists accept, is not always encashable. The value of a donor kidney finding its way to a patient in need of a match, for example. Or of a doctor joining a hospital where her skills save more lives than anywhere else. Or of a student getting into a college that’ll do his brain a good turn (yes, it happens). Or of a lifelong bond between two people (evidence of it is dodgy, but this happens too). Or of a hen warming an oddball egg that hatches into a flapper that learns how to fly (okay, this one is made up).
In all these cases, money-made matches would evoke horror.

Yet, the efficiency of allocations has always been the primary concern of economics. Without prices, though, how does one achieve market stability? To crack this conundrum of priceless pairings, Gale and Shapley devised a ‘deferred acceptance algorithm’. Consider their ‘marriage model’ of 1962. To kick off the season, each eligible man makes a proposal to an eligible woman, his first preference. Each woman assesses the offers she’s got, picks her top choice (or none at all), hangs on to it without saying ‘yes’, and rejects the rest. Any rejected man can then propose anew to someone else, his next preference. And a woman with a new proposal can replace her pick if she wants, rejecting the earlier one (since she’s allowed to hold just one). This goes on, round after round, until no further proposals are made; at this juncture, all women accept whatever offers they have. Everyone may not be entirely pleased with the outcome, but, as Gale and Shapley have shown, this results in ‘stability’—a concept that Roth later used to design other ‘match markets’—in the sense that it assures the best possible matches of mutual preference under the given proposal regime.

No doubt, the above example is of a male-dominated marriage market, and Gale and Shapley have also shown that a system with men making all proposals often leaves them pleased as punch—and women grumpy. For all its ‘stability’, the algorithm has an inherent bias one way or another (in female favour, if they act as proposers).

If that’s not enough of a letdown, closer scrutiny of this so-called ‘marriage game’ finds that proposees need not always be truthful about their order of preferences to get the best deal. Lying at some stage, in theory, may actually work to their strategic advantage; opting for a realistic rather than real choice, for instance. All this sounds suitably dismal. Alas, the math proves that no match stability mechanism exists for which being consistently truthful is everyone’s best option.
So, what’s the good news?

For one, these economists are under no illusion of having had a brainwave to overcome the ‘mutual misunderstanding’ that marriage is, as Oscar Wilde so eloquently described it. The Gale-Shapley marriage model is just a dummy, a way to frame a matchmaking problem. For another, their algorithm can be used to good effect for college admissions, B-school campus placements, organ transplants, job recruitments and in other such match markets. In all these fields, the idea is to bias the system in favour of applicants, not institutions, by having ordinary folk make the proposals.

This implies a profound power shift. And Gale-Shapley and Roth turn out to be bias busters (or overturners) after all… even if it was America’s bra burners of the 60s who led the way to this bias reversal. It was feminists who first dared to bust the male monopoly on sexual propositions, marital or not, no?