Optimal dating strategy and The Weekly Nabe

Don’t get too excited – this post isn’t about my dating life.

My supervising doctor and I sometimes have free-wheeling conversations, where the topic will bounce around randomly. Last week, it turned to optimal dating strategy: specifically, how long should you date around before you pick a mate?

Let’s assume you have a population of 100 potential spouses. You know nothing about any of them, or the range of their “value”, but you want to maximize your odds of picking the best. You randomly select one; after gauging him or her, you have to commit to marriage or leave that person. Once you’ve said “no”, it’s irrevocable.

If you found the previous paragraph confusing, or you don’t like the idea of quantifying people you date, here’s a different approach. There are 100 slips of paper in a hat, and on each is written a dollar amount. You don’t know the range of the values on the slips. After you pick a slip, you can accept it, or throw it out and pick another.

So how many do you have to see to get an idea of what’s available? 20? 50? 75?

Unsurprisingly, this has been tackled mathematically. (Don’t chuckle – I do know some math nerds who have impressive dating résumés.) Those of you so inclined can check out the article by Gilbert & Mosteller (1966).

The answer in this case is 37. You go out with 37 people, decline each, and then pick the next person who is better than all of them. The trick is to divide the size of the population by Euler’s constant (e ≈ 2.71828). Here, 100/e ≈ 36.7879.

This is where the blog comes in. How many neighborhoods do I have to see to get a sense of the range? 80/e = 29.4304. If I were looking for the best neighborhood according to this paradigm, I’d start with my next neighborhood, #30.

Finding the best neighborhood is not the point of the blog, of course, but I found the irony too juicy not to share. Plus, maybe this post will be reassuring to my single readers.

One last note: in both cases, by following optimal strategy, the probability that you end up with the best of the entire bunch is around 37%. Not great, but you can’t do any better.

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