Hiring the best candidate when you cannot go back

Question

You must hire exactly one person from 100 candidates. They arrive in random order and you interview them one at a time. After each interview you can rank that candidate against everyone seen so far, but you know nothing about the ones still to come. You must decide immediately: hire this person (and stop) or reject them (forever). You only care about hiring the single best candidate; second best is worthless to you. What strategy maximises the probability of hiring the best candidate, and what is that probability?

Accepted Answer

Reject the first 37 or so candidates (about 100/e), then hire the first one who beats everyone seen so far. The chance of getting the best candidate is about 1/e, roughly 37 per cent. Why a "look, then leap" rule. Early on you have no basis for judgement; late on you risk having passed the best. The natural rule is: use the first k candidates purely to set a standard, then hire the first later candidate who exceeds that standard. Probability of success. The best candidate is at position i with probability 1/100. With the rule above you hire her exactly when i is beyond k and the best of the f…

Hiring the best candidate when you cannot go back

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