…or why you shouldn’t settle down until you’re at least 27.
Another of my favorite math problems is the secretary problem. Let’s say that you’re trying to hire a secretary. You have n applicants for the job, and you know a priori that you have a strict ordering of the candidates once you’ve seen them (i.e. if you’ve seen m candidates, you can rank them in order), but you’ll see them one by one in a random order, and for each applicant, you have to decide to hire him/her or else reject him/her forever. What’s the strategy to choose the best candidate?
It turns out, the optimal solution is to automatically reject the first n/e candidates (where e is the base of the natural logarithm), and then to accept the first candidate who is better than everyone you’ve already seen. In essence, you recognize that you need to have a training set of a certain size to learn what’s out there, and then you hope that you can find someone who’s better than everyone in your training set.
This means that you shouldn’t settle down with your first boyfriend/girlfriend since he/she is probably not the best person out there for you, even if he/she seems wonderful at the time. You don’t have anything to compare to, so you don’t know if your first is the best match for you. This seems to be supported by the fact that the younger you marry, the more likely you are to divorce.
Applied to real life, let’s say that you start seriously dating at age 20 and you have 20 years of prime dating years (okay, this maybe isn’t practical for woman). But 20/e ~ 7, so you should date until you’re 27, and then marry the next person that you find who’s better than everyone else you’ve dated so far.
Of course, there are caveats to this: this strategy maximizes the probability that you choose the best candidate instead of optimizing the expected value of your mate (you wind up with the last person you see the 37% of the time that the best person was in the first n/e that you automatically rejected); in real life, once you say no to someone, you don’t necessarily say no to him/her forever (see the reasonably enjoyable romcom What’s Your Number?); you can’t necessarily provide a strict ordering of your mates, etc. You can also learn about relationships from observing others, so you don’t necessarily have to date someone to know if he/she’s good for you, and you can potentially get your training set vicariously, so maybe you can know whether or not the first person that you date is better or worse than the average relationship that you’ve observed second-hand.
Anyway, I know this strategy is likely to be much more controversial than my first tenet of dating efficiently, but personally, I think it means that I won’t be completely comfortable settling down until I’m at least a little bit older. What are your thoughts about the need to wait until you’re older before settling down permanently?