This is great; however, I don't quite understand how you can 'be stuck with' (i.e. choose) the second-best option if the very-best occurs in the first 37%... Surely you wouldn't be able to realise/decide that there is no one better than the best from the first group, if that is the case, until the end — by which point it's too late?
If you follow the rules of the equation, if you get to the end, you're marrying the last person you dated.
However, as noted in the article and by yourself, real life is never so constricting as only allowing you one chance at any particular person.
On the other hand, once you've passed on someone, there's nothing to guarantee that you'll be able to go back (they could be engaged, have moved away, hate your guts for evaluating mates by a mathematical formula, etc).
The scenario is that passing on a candidate means they might become unavailable, or choosing one means you can't look at the rest. Basically, how to choose the best item when you have to choose and can't change your mind?
Well, you can't guarantee you choose the best, but you can try to maximize the chance of doing better than random.
This models real-world situations such as (the article example) picking a wife from a pool of women, or even something such as who to hire from a pool of job applicants. In these scenarios, job candidate you passed on might take a different job, or the woman you choose to marry means you can't date the rest, or vice versa.
Obviously, if you can examine everyone and then go back and choose, you'd do that.
The irony is Kepler actually did get to go back - he hesitated on #5, she became unavailable, then he went through the rest of his list of women... and went back to re-woo #5. So he got to see all the candidates before choosing. ;)
Suppose the case of interview for a job where half the applicants are unqualified. This algorithm has an ~20% chance of hiring someone unqualified.
This algorithm seems optimized towards getting near-optimum rather then limiting risk. I think for real world problems it'd be much better to lower your standards as you near the end of the pool.
I think that's right. The only way you can choose the second best (and know it) is if the best occurs in the first 36% and the second best candidate is the very last one (if the best occurs in the first 36%, you'll always end up with the very last candidate, since nobody will satisfy the criterion of being the best so far).
You can unknowingly happen to choose the second best if the best candidate occurs among those you never consider because the second best is the best 'so far' when you get to them.
But the way it's described in the article is incorrect, as far as I can tell.
Am I missing something? Surely...