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dankuck comments on The application of the secretary problem to real life dating - Less Wrong Discussion
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The secretary problem is way overused, and very rarely has any application in practice. This is because it maximizes the probability of finding the best match, and NOT the expectation over the utility of the match your get. This is almost never what you want in practice; in practice, you don't care much between a match with utility 1000 and a match with utility 999, you just want to avoid a match with utility -1000.
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.