An interesting problem in decision theory. There are n applicants for the post of secretary. The applicants are randomly ordered and each is interviewed in turn until an appointment is made. Before each interview, the employer must decide whether or not to appoint the previous applicant. The employer cannot subsequently decide to appoint a previously interviewed applicant. It turns out that the strategy that maximizes the probability of appointing the best secretary is to interview the first e−1 (~37%) of the applicants, and then to appoint the first subsequent applicant who is superior to all those in the first group. If there are none, then the employer is left having to appoint the nth applicant.
Subjects: Probability and Statistics.