Secretary Problems

The classical secretary problem involves n secretary job applicants who can be ranked by a total order. The applicants are interviewed one by one in some random order. After each interview, the applicant is accepted or rejected. The decision is based only on the relative ranks of the applicants interviewed so far. The game has payoff 1 if the best applicant is selected and 0 otherwise.
The solution is to interview the first n/e candidates and then hire the first that is better than the first n/e candidates. For large enough n, the probability of success is 1/e.

Today, Nicholas Georgiou gave an interesting talk where a general partial order on candidates is considered instead of a linear order. He presented a strategy where the probability of success is 1/4. Check out the paper.

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