### Satoshi Kanazawa

The Scientific Fundamentalist

# Why Dating Is Difficult in New York (or London)

## There is a mathematically proven best way to date.

Posted Oct 25, 2009

The guest blogger and PT intern Jen Kim complains about the difficulties of dating in New York.  No wonder she finds it difficult.  Since 1966, it’s been mathematically proven that dating in New York is difficult....

In their 1966 paper entitled “Recognizing the Maximum of a Sequence” published in the Journal of the American Statistical Association, John P. Gilbert and Frederick Mosteller offer a solution to a problem known as the “beauty contest problem.”  This is how Gilbert and Mosteller describe the problem.

Suppose a boy is to have a date with his choice of one of n unseen and unknown girls, and suppose he wishes to choose the prettiest.  The girls are presented for him to see one at a time in a random order, and he must choose or reject a girl when she appears.  Once he chooses, he sees the rest, and he is disappointed if his date is not the prettiest.  How can he maximize his probability of choosing the prettiest of the lot?

Of course, we know by now that, for any mammalian species, including humans, it’s not the boy who does the choosing, but the girl (like Jen).  But the mathematical problem remains exactly the same if you swap “boy” and “girl” in the above quote and call it the “resource contest problem” or “The (sequential) Bachelorette.”

In the paper, Gilbert and Mosteller prove (yes, this is mathematics, not science, so there can be absolute proofs) that the optimal strategy is to reject the first 37% of all the candidates, and then select the first candidate who is better than any previous candidate.  Gilbert and Mosteller prove that, if you follow this strategy, you will choose the best of all possible candidates on average about 37% of the time.  You may think that 37% chance is not very good, but there are no other strategies that you can consistently follow that will produce a higher average probability of choosing the best of all candidates.  So this is the optimal strategy for maximizing the quality of your chosen mate.

Now the problem for Jen and millions of other single women in New York becomes clear.  If you live in Ames, IA, you can expect to meet, say, 10 men – 10 potential husbands – in your life.  In that case, your optimal strategy requires you to reject the first four men (no matter who and how good they are) and then marry the first man who is better than any of the ones that you have dated before.  If you live in New York (or London), you can expect to meet, say, 1,000 men.  Now your mathematically proven optimal strategy requires you to reject the first 369 men (as n approaches infinity, the precise number to reject becomes n/e) and marry the first man who is better than any of the hundreds of men who came before.

Remember, in order to determine who the first man is who is better than all the ones who came before, you have to evaluate each of your dates very carefully.  It’s not like you can just hang up on the phone calls or delete the email messages from the first 37% of the suitors.  You actually have to go on dates and talk to them and evaluate how good they are (even though you know that you will automatically reject the first 369 men).  So you have to go on at least 369 separate dates in New York before you can even begin to consider each candidate seriously for marriage.

That’s why dating in New York is much more difficult, exhausting, and time-consuming than dating in Ames.

Now switching gears from mathematics to evolutionary psychology, given that this strategy is mathematically proven to be optimal, the logic of natural selection suggests that, over a long period of human evolution, all women will eventually be selected to employ this strategy, without being consciously aware of the mathematics behind it.  Women who adopt the “Reject the first 37% and choose the next best” strategy are expected to achieve greater reproductive success on average than women who adopt the “Marry the first one I can find,” or “Reject the first 5% and choose the next best” or “Reject the first 90% and choose the next best” or any other potential strategy.  Unconsciously, all women should have the evolved psychological mechanism to reject the first 37% of the total estimated number of lifetime potential mates, and choose the next best candidate.

While it is often difficult to estimate the precise number of lifetime potential mates that a woman will encounter in her life, it is safe to assume that she will encounter many more in a large metropolis than in a small town.  This can therefore explain why women remain single longer and marry later in New York than in Ames, and, in general, why women in urban areas (with a greater number of potential mates) remain single and marry later than women in rural areas (with a smaller number of potential mates).