The secretary problem ( 1, 2, 3, 4, 5 ) optimal stopping, says "stop and keep the best" in a randomized sequence of known length "k" where you can't select previously elements of the sequence.
One stopping criteria says "go through 37% of the total sample, then select the next element that is higher in value than the best of your pool. The "then select" indicates a transition in behavior.
What are the "considered pretty good" options for the transition?
Threshold (n) options that I know of include:
- change the threshold from 37% to some other percent, so sample a larger or smaller constant percentage sample of the total population.
- make the threshold a constant times the square root of the total sample count, so non-linear sampling based on pool size. This is going to give faster selection for larger pools, but might not be as likely to give highest average performance.
Options for the "who to select after transition" are a different question. I have seen mean, max, median, or quantile options here. Surprisingly enough the other considerations that come into play are hiring rate vs time, gap, and distribution of hired talent in the iterated version of the problem.
Can you point me to others that folks who have explored the problem consider "pretty good", "competitive" or otherwise decent?
If there aren't options, why not?
