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dankuck comments on The application of the secretary problem to real life dating - Less Wrong Discussion
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Does the secretary problem say anything about getting the second-best match? That seems to be the crux and this is the counter-argument I'm most swayed by.
https://en.wikipedia.org/wiki/Secretary_problem#Cardinal_payoff_variant
is an interesting alternative. But still not great, basically choose the best candidate after sqrt(n) and a non-trivial sqrt(n) chance of ending up at the last candidate.