Secretary Problem

I learned about the secretary problem recently and found it extremely profound. 🙂

Imagine an administrator willing to hire the best secretary out of N rankable applicants for a position. The applicants are interviewed one-by-one in random order. A decision about each particular applicant is to be taken immediately after the interview. Once rejected, an applicant cannot be recalled. During the interview, the administrator can rank the applicant among all applicants interviewed so far, but is unaware of the quality of yet unseen applicants. The question is about the optimal strategy to maximize the probability of selecting the best applicant.

The solution is 36.9%

In my case, I have applied it to my hiring process. I think that I have found someone to hire as a full-time staff and I have made the offer. Extrapolating the problem further, it means that every hire that I make from now on, will need to be better than the last.

I think that this is a good policy to have as it will inevitably ‘raise the bar’ when it comes to my hires. Hiring continuously better people will result in an upward trending average capability within the company.

One might think that this problem can be applied to the problem of finding a mate.

At first inspection, it seems like a good idea but it fails on one assumption – that the person who applied for the position actually will take the position if accepted. In the case of a mate, that may not be the case as an offer made can often result in rejection.

Interesting little bit of math though.

Published by

Shawn Tan

Chip Doctor, Chartered/Professional Engineer, Entrepreneur, Law Graduate.

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