How to Get a Bead on Your True Love

My grandmother spent her whole youth hearing that she should stay away from strange men. Then she went and married one. But our family had a secret: She was a little strange, too. The two of them together were perfection.

Great matches have inspired philosophy and verse for as long as we have possessed charcoal to scratch with. But before a match can be celebrated, it has to happen. How do people do it? How do they sort through all the potential mates and find their true loves?

So often, it seems impossible. But to an economist, the most striking characteristic of sublime matches is that they are ubiquitous, in both society and nature. In fact, if Easter has the bunny, then Valentine's Day should have the albatross.

Like humans, albatrosses often mate for life, but only after a lengthy period of awkward dancing. They nest on remote oceanic islands, where their hatchlings take up to 10 months to mature. The birds can live more than 50 years, and a nesting pair will return to the same site year after year. But when one of them dies, a funny thing happens: The surviving partner will often find a new partner that has also lost its mate.

A large brooding colony has hundreds and hundreds of, shall we say, chicks, so you have to wonder: Exactly how do these birds find one another? How do they sort through all the possible matches and find such perfect partners?

As daunting as that challenge may seem, the fact is that humans face a much steeper hurdle. If you're not a numbers person, you might not have noticed how awe-inspiring the matching problem is.

There are approximately 6.7 billion people on earth. But finding your perfect mate is not as simple as evaluating the attractiveness of each world citizen one by one. Their feelings matter, too. A relationship worthy of song only happens when you are the best possible match for your mate, and he is the best possible match for you.

That little qualification makes the marriage problem almost unfathomable. The number of possible pairs of two in a population of 6.7 billion is very, very large, and an omniscient observer could find the best partners only by inspecting each and every possible match. There are 28 million times more possible romantic matches among people in this world than there are stars in the Milky Way. If God spent a minute evaluating each match before assigning people their spouses, the procedure would take 21.4 trillion years to complete. By then, the chocolates would be stale.

So how does it work?

Economists have made a science of studying the mechanisms humans have developed over time to achieve good matches. The pioneering work was published in 1962 by David Gale and Lloyd Shapley and was titled "College Admissions and the Stability of Marriage." They explored the question of whether a population of men and women could be sorted into stable "marriages" -- that is, pairings that would not be dissolved by defection. A marriage would dissolve if there were alternative interested partners whom each spouse would prefer to their own.

The revolutionary accomplishment of Gale and Shapley is that they proved that a simple algorithm could produce a stable set of matches that assign everyone a spouse. You might say that they proved with math that there is someone for everyone.

The algorithm, which was a purely theoretical construct, is simple and eerily reminiscent of historical social convention. Suppose that we put 10 men and 10 women, all heterosexual, in a room. The Gale-Shapley algorithm would assign their mates as follows: The men line up and, one by one, propose to their favorite woman. The women can either reject the proposal or defer it until the next round by becoming "engaged." In the next round, each unengaged fellow tries again with his next favorite woman. A woman who was previously engaged can ditch her fiancé and become engaged to her new suitor if she wishes. The game continues until everyone is engaged, at which point, in cult-like fashion, everyone is married all at once.