Solving optimal stopping problems with statistical algorithms
The saying goes that you should quit when you're ahead. Making a decision on when to conclude a selection process is often not that easy in real life. In mathematical statistics, a puzzle known as the "secretary problem" [1] sums this up nicely. A number of candidates are applying for a secretary position at a company. In the selection process, the employer must decide after each interview, whether to accept the candidate or reject them and hope for a more suitable applicant later on. The decision is final, the employer is not allowed to invite back any rejected applicants.
An employer who is thinking logically should carefully check the first few candidates and not simply take the first one. Later, when the line starts to come to an end, the employer will possibly take on a more-or-less suitable candidate for fear of being left with only unsuitable candidates, and – not having any other options – grudgingly just bite the bullet, and grab whoever is left.
Ideal: 37 Percent
How should the employer proceed to mathematically ensure the best possible odds of finding an above-average candidate? How long should the try-before-buy phase last, in which the employer explores the unknown capabilities of candidates before immediately snapping up the one that is better than all the previous ones and hopefully scores favorably against future candidates further down the line? Mathematicians have been tackling stop problems [2] for thousands of years.
[...]
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