MEB + ARK, a.k.a. the Haystack Hunters, wrote the following:
As fans of your work in real life probability and breaking the law of averages, we were hoping you could apply your theories to the most perplexing problem of all: true love. According to some recent articles, the pool of eligible, educated, single males aged 27-37 is dwindling, while the number of equally eligible women is climbing so with the odds stacked against us how to we go about finding our “One.” Is there any way to fix the numbers in our favor? As writers we can barely balance a check book, let alone weigh the odds of finding our perfect mate particularly since he’s one in a million (read: above average) and we’re both one of a kind. So how do we solve life’s most essential equation: i + u = xoxoxo? We’re quite serious about our search and would so appreciate any statistically proven insights.
Statisticians are, as everybody knows, the best people to ask about matters of the heart. And if statisticians in general aren’t, I am. After all, everybody loves me. When you think of me, you think of amour; or is it amour-propre?
Anyway, there is in probability a classic conundrum called the Marriage Problem, which is applicable to your request. Sort of. By which I mean the Marriage Problem gives an approximation about how many men you should go through before stopping at the one you have in your hands and latching onto him permanently.
Assume you know you have N date-worthy men swimming before you. You can date one at a time. You can keep the current one, or discard him forever hoping to find a better one later. You also must know all there is to know about all the men such that you could rate their marriageability unambiguously. That is, you must be able to rate them, from least to best.
If you know there’s only one guy whom you can date, then the solution is obvious: marry him. If there are two, then if you don’t like the first guy you must marry the second. The chance number-two is better (or worse) is 50%, which is thus the chance that you make the best marriage.
Surprisingly, this same strategy—dumping all suitors hoping to find a better later—gives a 50% chance of finding the best mate if there are three dateable men. And it gives about a 40% chance of finding the best mate if there are as many as ten men. Pretty good!
How many men should you consider before stopping? Well, it’s all been worked out (a good explanation is here: pdf)
For every value of N—which you assume you know without error—here are the optimal number of men at which you must stop. Also shown in the probability (rounded to the nearest hundredth) for each stopping value. After N is larger than 3, this probability varies little from 40%—as N increases to very large numbers it levels off at 37%. Meaning you have a pretty good shot at finding your optimal mate if you follow these rules.
For example, assuming you know that you can date as many as N = 7 men in your lifetime, you should date the first man then drop him (abruptly, if he doesn’t call), but you should keep the next guy that is better than the first, and also drop the others after the first who weren’t as good as the first. If you do this, you have a 41% of finding True Love.
Of course, it could have been that the first guy was the best. What happens then is you end up going trough the other 6, one by one, your despair increasing with each new suitor. Finally, you’ll land on number 7 with whom you’re stuck—unless you choose spinsterhood and consider a houseful of cats an appealing alternative. All you can do is pray that the seventh guy wasn’t the worst in the bunch.
The problem with this table is that it assumes you know the value of N, which most people living outside a prison or desert island don’t. N could be large or small, depending on life’s vicissitudes and the number of marriageable men who live within easy reach.
The following pictures help account for the uncertainty you have in N.
I still assume (for illustration) that the maximum number of men is 20, but that you don’t know you’ll have as many as that. If could be that you believe that you will only meet about one to five dateable guys. More are possible, but not probable, especially above 10. Call this the San Francisco, or Sparse scenario. This is pictured in green.
This scenario says that you think there is about a 15% chance you will see only N = 1 dateable man, but there is also 23% chance you will see N = 2 dateable men, and so on. If this picture represents your uncertainty in N, then your optimal stopping point is 1. Marry the first guy, whether he agrees to meet your mother or not.
The second scenario is the Midwest or Average view. You believe there will be a maximum of 20 men, but the most likely course is that you will know N = 9 or N = 10 dateable men (about 13% chance each). It’s possible, you think, that will only know just 1 dateable man, or even 20 men, but each possibility is remote (less than 1% chance for either). In this case, you should stop at 3.
That is, reject the first guy, then all the others that are worse than him, but then also drop the very next guy better than him. Tease this improved-over-number-one guy for while if you like, but move on. Reject all other suitors that are worse than all that came before, but keep the very next one that is better.
The last view is the New York or Thick scenario. This is where you believe that there are as many as 20 dateable men, and where you also think that the chance you can see them all (if you wanted) was high (about 16% chance for 19 or 20). Seeing just 1 dateable man is possible, but unlikely. Here you should date a lot, and drop most of them like last year’s handbag, until the sixth guy who was better than all who came before. Keep him. He will be Mr Right.
But only if this model truly represents reality. Which it probably doesn’t.
For one, it assumes that you can’t reconsider those who you have previously dumped, that men are constant in their behavior and their rankings fixed. As you date you age, so it’s likely that future men you date will begin to look better than they looked when you were younger. The model also assumes you don’t change, and that the man isn’t using the same strategy as you are.
How to account for all these (and other) contingencies is unknown, so it appears that the safest bet is not to be too picky.