Part 2 of The Physics Guide to Hooking Up: Why It's Better to Pursue than to be Pursued, or the Trouble with Rule 6

I'm sorry to burst the bubble of any Disney fans out there, but Prince Charming almost certainly lived more happily ever after than Snow White did.

I'm saying this horrible thing because a famous mathematical puzzle known as the Stable Marriage Problem shows that a person who pursues a mate is almost always more satisfied with their spouse than a person who is pursued.

This is a particularly important fact for women who adhere to The Rules, because physics and math suggest that rule number 6 of the top ten rules for women appears to be very, very wrong.


Skip to the Tip in this week's post.

The first analysis of the Stable Marriage Problem was described in a 1962 paper by mathematician David Gale and economist Lloyd Shapley. They were attempting to determine if a set of 100 men and 100 women could pair up in marriages in a way that no one could find a better mate in the bunch who would have them.

They way they set up the problem goes like this . . .

Each man ranks all 100 women from their first choice of potential partner to their last. The women all do the same for the men. Because the reasons one person finds another attractive is often mysterious, Gale and Shapley selected each person's ranking of potential mates at random. As a result, no two rankings were alike and one person's top choice would likely be farther down on any other person's list. Once everyone has their ranked list, the marriage game begins.

Probably because the paper was written way back in 1962, pairings among men and women occur when a man proposes and a woman accepts. To begin with, the first man proposes marriage to the woman at the top of his list. Because it's early in the game and this is the only marriage proposal the woman has gotten, she accepts (remember, it's just a simple model).

Once the first pairing is out of the way, the second man proposes to the top woman on his list. Assuming she's not engaged to the first man, she accepts. If, however, she happens to be the fiancé of the first man, the woman looks at the ranking of her two suitors and chooses to go with the one she ranked highest.

The game continues with each man in turn proposing to women in the order that he ranked them. As he goes down the list, a woman will accept his proposal if she is either unattached or engaged to a man who she ranks lower than him. Any man who has been thrown over for a higher ranking fellow eventually goes back down his list looking for a woman who is single or prefers him to her current fiancé.

Gale and Shapley found that there are always stable solutions to the problem (usually many solutions, in fact), regardless of the number of people involved. Stability in this case means that once everything is sorted out, a man who checks out all the other couples in the group would not find a woman he prefers over his own fiancé who also ranks him higher than her fiancé.

Mathematically speaking, that's a pretty interesting result. But it's not terribly useful or informative for real people like you and me. The truly fascinating revelation, in my opinion, is that something very surprising comes out of the study if you consider the relative satisfaction of men and women in the model. Specifically, if you look at the ranking of the women who the men ended up with, most men got engaged to a woman who was high on their list. Women, on the other hand, were stuck with men who ranked relatively low on their lists.

To put hard numbers on it, in an expanded a study of 1000 stable solutions to the problem when it included 512 couples, men on average hooked up with women who ranked 8th on their respective lists, while women were engaged to men who ranked an average of 80th. That's a huge discrepancy. Bear in mind that the only difference between men and women in the mathematical model is that men always proposed and women only accepted or rejected proposals.

You'd be right to take all this with a grain of salt. Mating in real life is a much more complicated affair. Even a slight modification of the problem, such as adding the potential for degrees of inherent beauty among the men and women, can radically change the numbers of stable solutions and the average degree of satisfaction. (Some realistic details can actually make the problem so complex that it's essentially unsolvable.) Nevertheless, in general when only men made proposals they were much better off than the women.

The world has changed a lot since '62. Back then, the Stable Marriage Problem didn't have a lot of relevance to the actual complexities of dating and mating. These days, there is one situation that pretty closely approximates the bare-bones problem that Gale and Shapley studied - online dating services.

When you join Yahoo Personals or some other matching service, you post your profile and often your picture. You then have a choice; you can sit and wait for invitations (for dates usually, rather than marriage) to come rolling in, or you can check out the profiles of other people and decide who you would like to contact.

If you passively wait for someone to write to you, you mimic the behavior of the women in the Stable Marriage Problem. That is, you sit on your hands waiting for an email or an instant message from a suitor, then you check out their profile and either accept or reject them.

If instead you take the initiative, you act like the men in the Stable Marriage Problem. You perform some sort of ranking and choose the person you want to contact most from all the people who have posted profiles. If the first person you write to rejects you, you are forced to move farther down in your list of possibilities.

According to the solutions of the Stable Marriage Problem, if you take the initiative in asking out the people you're most attracted to you will meet much more desirable people through online dating services than you would if you wait for someone to contact you.

This runs completely counter to rule number six of the top ten rules for women, which reads "When considering whether to use personal ads or other dating services, you should place the ad and let men respond to you."

Don't get me wrong, I think many of The Rules work just fine. Most of the rules will help a woman play a man like a starving trout hooked on a line. But if you ignore rule six and take the initiative in luring a mate, you dramatically increase your odds of landing a trophy catch rather than some loser you'll want to heave back into the pond.