The Eligible-Bachelor Paradox

Actually, no?-and here's why. Consider the classic version of the marriage proposal: A woman makes it known that she is open to a proposal, the man proposes, and the woman chooses to say yes or no. The structure of the proposal is not, "I choose you." It is, "Will you choose me?" A woman chooses to receive the question and chooses again once the question is asked.

The idea of the woman choosing expressed in the proposal is a resilient one. The woman picking among suitors is a rarely reversed archetype of romantic love that you'll find everywhere from Jane Austen to Desperate Housewives. Or take any comic wedding scene: Invariably, it'll have the man standing dazed at the altar, wondering just how it is he got there.
Obviously, this is simplified?-in contemporary life, both sides get plenty of chances to be selective. But as a rough-and-ready model, it's not bad, and it contains a solution to the Eligible-Bachelor Paradox.

You can think of this traditional concept of the search for marriage partners as a kind of an auction. In this auction, some women will be more confident of their prospects, others less so. In game-theory terms, you would call the first group "strong bidders" and the second "weak bidders." Your first thought might be that the "strong bidders"?-women who (whether because of looks, social ability, or any other reason) are conventionally deemed more of a catch?-would consistently win this kind of auction.

But this is not true. In fact, game theory predicts, and empirical studies of auctions bear out, that auctions will often be won by "weak" bidders, who know that they can be outbid and so bid more aggressively, while the "strong" bidders will hold out for a really great deal. You can find a technical discussion of this here. (Be warned: "Bidding Behavior in Asymmetric Auctions" is not for everyone, and I certainly won't claim to have a handle on all the math.) But you can also see how this works intuitively if you just consider that with a lot at stake in getting it right in one shot, it's the women who are confident that they are holding a strong hand who are likely to hold out and wait for the perfect prospect.

This is how you come to the Eligible-Bachelor Paradox, which is no longer so paradoxical. The pool of appealing men shrinks as many are married off and taken out of the game, leaving a disproportionate number of men who are notably imperfect (perhaps they are short, socially awkward, underemployed). And at the same time, you get a pool of women weighted toward the attractive, desirable "strong bidders."

Where have all the most appealing men gone? Married young, most of them?-and sometimes to women whose most salient characteristic was not their beauty, or passion, or intellect, but their decisiveness.

Evolutionary psychologists will remind us that there's a long line of writing about "female choosiness" going back to Darwin and the male peacocks competing to get noticed by "choosy" mates with their splendid plumage. But you don't have to buy that kind of reductive biological explanation (I don't) to see the force of the "women choose" model. You only have to accept that for whatever socially constructed reason, the choice of getting married is one in which the woman is usually the key player. It might be the man who's supposed to ask the official, down-on-the-knee question, but it usually comes after a woman has made the central decision. Of course, in this, as in all matters of love, your experience may vary.

There may be those who look at this and try to derive some sort of prescription, about when to "bid," when to hold out, and when (as this Atlantic story urges) to "settle." If you're inclined to do that, approach with care. Game theory deals with how best to win the prize, but it works only when you can decide what's worth winning.

BM

I don't buy it.

These days marriage is not as valuable to men as it was. Single men gain fewer advantages by marrying then before... so there is not much pressure on men to marry. I don't think men settling for "less valuable" women is a factor-- my observations are consistent with this.


I propose the real phenomenon is that in general men marry younger women. Couples where the woman is older than the man have always been rare.

Let's consider a woman who was born in 1970. She likely will end up coupled with a man born in 1965 (or before). Of course there are fewer men born in 1965 then women born in 1970 (due to population increase).

So in each mating cohort (on average older men and younger women).... there are more women than men. This means after the "desirable" men are taken there will still be some "desirable" women left over.

I attribute this to the age shift in mating couples.

Does this belong in the Mathematics forum?