Optimal stopping behavior with relative ranks: the secretary problem with unknown population size
Darryl A. Seale, Amnon Rapoport · Journal of Behavioral Decision Making · 2000
We examine multi-period observation and selection problems with an unknown number of applicants in which applicants are interviewed one at a time on each period, recall of applicants that were interviewed and rejected is not possible, the decision on each period to reject or accept an applicant is based on relative ranks, and the objective is to maximize the probability of accepting the top-ranked applicant. We propose and then assess the efficiency of three descriptive models by simulation, and then test them competitively in a computer-controlled experiment. A cutoff decision model, in which the first r−1 applicants are rejected and then the first applicant who is ranked higher than all previously observed applicants is accepted, outperforms the two other two models. Compared with the optimal policy, subjects stop the search too early. Their behavior is accounted for by a cutoff model that postulates an endogenous cost of search. Copyright © 2000 John Wiley & Sons, Ltd.