The 1/e concept doesn't quite apply. First of all, the "Secretary Problem" assumes a binary payoff structure: +1.0 for getting the absolute best and 0.0 for getting anyone else (and maximizes the EV at 1/e). However, for most people, getting the 2nd-best theoretical potential mate is quite a bit better than ending up alone (especially because people and preferences change, making the concept of "best potential mate" sketchy; the person you want most at 17 is probably a bad lifelong match.)
Let's look at it, though. For the first 15-20 years (subject to debate) you don't know anything about this problem. You don't know who you are, everyone's changing fast, you're blinded by sexual desire, etc. For the last 30 years, your reproductive viability is reduced for men and zero for women. This puts the "choosing window" at, say, 20 to 50. That would mean that one doesn't settle down until 32 at the absolute earliest, and that most people would do so in their 40s (and have only a few years to bear children). Most people don't want to wait that long to settle down, and for good reasons.
One major one is that the pool of available singles declines in quality as you get older. The Secretary Problem assumes a uniform distribution of quality over time. It's not true (and, in fact, insulting) to say that "all the good ones are taken", but I definitely noticed a change in the average quality of dates from 20 to 26 (when I met my wife and left the dating game). You still can find great people at any age, but the distribution evolves. Because people improve with age (fuck VCs and how they think about that) there's some push at the high end, but that's not offset by the disproportionate rate at which either (a) "the good ones" are taken, or (b) the messed-up people become better at hiding themselves, which is my preferred theory.
(I have no idea whether that decline of available mate quality continues after 26, or if it levels off or even reverses. I know some high-quality people who are single at 40, but have no concept of the aggregate dating scene at that age.)
Empirically, people don't "hold out" during 1/e of their window because, unlike with the Secretary Problem, the payoff in choosing the 2nd or 3rd-best theoretical match is quite high (maybe 0.8 to 0.99) compared to the payoff (0.0 by definition) of never meeting someone as good as the best during your hold-out period.
> Empirically, people don't "hold out" during 1/e of their window because, unlike with the Secretary Problem, the payoff in choosing the 2nd or 3rd-best theoretical match is quite high (maybe 0.8 to 0.99) compared to the payoff (0.0 by definition) of never meeting someone as good as the best during your hold-out period.
The 2nd or 3rd-best theoretical match could also have a negative payoff (divorces you, takes half your money + child support + alimony). You can lose a lot more marrying the wrong person than never marrying at all.
Wow if that's true then marriage is just a horrible bet. Let's say you would date 10 potential marriage partners - you're saying that only one of them would have an outcome better than divorcing you and taking half your money and your kids? I wouldn't even consider marriage as a possibility if the odds were that bad.
There is a variant of the secretary problem that assumes a different payoff structure - each secretary has a payoff which is uniformly distributed U(0,A) for unknown A. As I recall, the stopping time is O(sqrt(N)).
The bigger difference is that there is no set time where you have to choose whether to marry someone. You can, for example, go back to dating someone you dated previously and then decide to marry them.
Let's look at it, though. For the first 15-20 years (subject to debate) you don't know anything about this problem. You don't know who you are, everyone's changing fast, you're blinded by sexual desire, etc. For the last 30 years, your reproductive viability is reduced for men and zero for women. This puts the "choosing window" at, say, 20 to 50. That would mean that one doesn't settle down until 32 at the absolute earliest, and that most people would do so in their 40s (and have only a few years to bear children). Most people don't want to wait that long to settle down, and for good reasons.
One major one is that the pool of available singles declines in quality as you get older. The Secretary Problem assumes a uniform distribution of quality over time. It's not true (and, in fact, insulting) to say that "all the good ones are taken", but I definitely noticed a change in the average quality of dates from 20 to 26 (when I met my wife and left the dating game). You still can find great people at any age, but the distribution evolves. Because people improve with age (fuck VCs and how they think about that) there's some push at the high end, but that's not offset by the disproportionate rate at which either (a) "the good ones" are taken, or (b) the messed-up people become better at hiding themselves, which is my preferred theory.
(I have no idea whether that decline of available mate quality continues after 26, or if it levels off or even reverses. I know some high-quality people who are single at 40, but have no concept of the aggregate dating scene at that age.)
Empirically, people don't "hold out" during 1/e of their window because, unlike with the Secretary Problem, the payoff in choosing the 2nd or 3rd-best theoretical match is quite high (maybe 0.8 to 0.99) compared to the payoff (0.0 by definition) of never meeting someone as good as the best during your hold-out period.