Sequential observation and selection with relative ranks: An empirical investigation of the Secretary Problem.

Abstract

Sequential observation and selection behavior was examined in the context of employer hiring decisions. The principal objectives of the study were to test the descriptive power of the optimal solution, find and characterize simple decision policies that subjects might use when confronted with these types of decision tasks, and examine the sensitivity of both optimal and non-optimal decision rules using computer simulation. In order to compare experimental and theoretical results, common assumptions of the Secretary Problem (SP), as well as the number of applicants, were systematically varied across three experiments. Experiment 1 investigated the standard version of the SP, where all of the usual assumptions were met. Experiment 2 relaxed the assumption that only the best will do, paying subjects for correctly selecting either the top or second-ranked applicant. Experiment 3 introduced uncertainty in the number of applicants using uniform distributions from 1 to 40, and 1 to 120 applicants for the experimental conditions. Several important results were described. First, the simulations showed that the optimal policy is rather insensitive to slight variation in r. Second, cutoff-type policies accounted for the decisions of a majority of subjects in every experiment and condition. Third, under certain conditions, non-optimal policies, particularly counting the number of successive non-candidates, performed remarkably well. Finally, subjects, generally, made their selection decisions too early (i.e., in advance of optimal prescriptions). The study concludes with a summary discussion of the findings, suggestions for experimental extensions, and a description of a methodological innovation for collecting individual decision data in future similar investigations.