Sequential Decision Making with Relative Ranks: An Experimental Investigation of the "Secretary Problem">

Abstract

The "secretary problem" models a class of optimal stopping decision tasks in which the binary decision to either stop or continue the search only depends on relative ranks. We present this problem in a computer-controlled experiment designed to investigate sequential observation and selection behavior in the context of employer hiring decisions. Our principal objectives are to test the descriptive power of the optimal decision policy; characterize and competitively test simple decision rules, or heuristics, that individuals might use in optimal stopping decision tasks; and examine the sensitivity of the various decision rules by computer simulation. Our simulation results show that the optimal policy is insensitive to moderate deviations from the optimal cutoff value, and that a simple, non-optimal decision rule that counts the number of successive non-candidates performs remarkably well. Model comparisons show that simple cutoff decision rules account for the decisions of the majority of the subjects. The observed tendency to stop the search too early is accounted for by postulating an endogenous cost of time spent in the search.