# Utility Mill

## Secretary_Problem_Optimizer

#### Instructions / Discussion

This utility will tell you the optimal number of candidates to interview given the total pool of applicants.

The secretary problem is an optimal stopping problem that has been studied extensively in the fields of applied probability, statistics, and decision theory. It is also known as the marriage problem, the sultan's dowry problem, the fussy suitor problem, and the best choice problem. The problem can be stated as follows:

1. There is a single secretarial position to fill.
2. There are n applicants for the position, and this is known.
3. The applicants are interviewed sequentially in a random order, with each order being equally likely.
4. The applicants can be ranked from best to worst with no ties.
5. The decision to accept or reject an applicant can be based only on the relative ranks of the applicants interviewed so far.
6. Rejected applicants cannot be recalled.
7. You will only be happy if you select the single best applicant. You get a payoff of 1 if you do so, and nothing otherwise.

Let us say that an applicant is a candidate only if it is better than all the applicants viewed previously. Clearly, since the objective in the problem is to select the single best applicant, only candidates will be considered for acceptance. One reason why the secretary problem has received so much attention is that the optimal policy for the problem (the stopping rule) has a surprising feature. Specifically, for large n the optimal policy is to skip the first n / e applicants and then to accept the next encountered candidate, where e is the base of the natural logarithm. As n gets larger, the probability of selecting the best applicant from the pool goes to 1 / e, which is around 37%. Whether one is searching through 100 or 100,000,000 applicants, the optimal policy will select the single best one about 37% of the time.

Notes

Selecting "Want Higher Value Applicant - Not best" uses this concept. The answer will always be sqrt(number or applicants) but I'll go ahead and calculate it for you anyway.

Utility Mill is another wonderful Blended Technologies project.

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