You never really have the "best", unless there are few candidates and one of them stands out. There are performance probability distributions. It would be tremendously helpful is someone with actual experience in hiring decisions could chime in with a real-world solution, rather than depending on mathematical theory of dubious value. -- Gene
________________________________ From: Charles Greathouse <charles.greathouse@case.edu> To: math-fun <math-fun@mailman.xmission.com> Sent: Tuesday, June 17, 2014 6:00 PM Subject: Re: [math-fun] secretary problem
The usual payoff for the secretary problem is 1 if you choose the best candidate and 0 otherwise, in which case you should never select a candidate if you've seen a better one previously. From this the optimality of the general strategy follows directly.
If you're using some other payoff scheme then it probably isn't optimal. For example if your payoff is 0 if you choose the worst candidate and 1 otherwise, you should select the first candidate who is better than the worst you've seen so far.
Charles Greathouse Analyst/Programmer Case Western Reserve University
On Tue, Jun 17, 2014 at 8:06 PM, Bernie Cosell <bernie@fantasyfarm.com> wrote:
I was just reading a PDF about the secretary problem and all of the analyses I've ever seen seems to start with the assumption that the optimal strategy will necessarily be of the form "examine the first K candidates and then take the first candidate better than any you've seen so far", and if you haven't picked any candidate before that you MUST pick the N'th. And the math goes from there to derive the usual N/e value for K.
What got me curious [and this has actually drifted in and out of my pondering for some time now] is whether there's a proof that includes proving that the *assumption* is correct, also. I could see a strategy, for example, where you examine K candidates and then take the *second* best [that is, wait until you get one better than K, and then take the one better than that second one]. There might be other strategies more subtle or something beyond my ken. I don't see how to prove the assumption: that that's the best *possible* selection strategy. ???
/Bernie\
-- Bernie Cosell Fantasy Farm Fibers mailto:bernie@fantasyfarm.com Pearisburg, VA --> Too many people, too few sheep <--
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