cute, and fair points; This feels like an attack on the whimsical anec-datas and choice of language that I threw in there to keep people amused and reading further; not the actual things that I wanted to share as content… Is that what you meant to do?
The first point seems like a genuine and substantial objection to the secretary problem’s framing of the issue.
You’ve sort of addressed it by suggesting that maybe we should try a bunch of partners and then choose the next one that’s better than 90% so far, rather than the best that’s better than all so far, but it seems to me that once you’ve noticed that P is the wrong problem you should be trying to figure out the right problem and solve that, rather than solving P and then applying ad hoc tweaks to the answer.
I believe people have analysed variants of the secretary problem where, e.g., each candidate has a quality score (drawn independently from some known distribution, I guess) and you want to choose a candidate to maximize expected quality.
[EDITED to add: I see that anon85 has made similar points.]
No, off the top of my head I can’t think of any situation where all possible choices other than the best are equally bad.
There are plenty of people the same age who don’t like the same music, too.
cute, and fair points; This feels like an attack on the whimsical anec-datas and choice of language that I threw in there to keep people amused and reading further; not the actual things that I wanted to share as content… Is that what you meant to do?
The first point seems like a genuine and substantial objection to the secretary problem’s framing of the issue.
You’ve sort of addressed it by suggesting that maybe we should try a bunch of partners and then choose the next one that’s better than 90% so far, rather than the best that’s better than all so far, but it seems to me that once you’ve noticed that P is the wrong problem you should be trying to figure out the right problem and solve that, rather than solving P and then applying ad hoc tweaks to the answer.
I believe people have analysed variants of the secretary problem where, e.g., each candidate has a quality score (drawn independently from some known distribution, I guess) and you want to choose a candidate to maximize expected quality.
[EDITED to add: I see that anon85 has made similar points.]
In my second paragraph, yes. In my first paragraph my point was like “garbage in, garbage out”.