When to stop — A cardinal secretary search experiment

Abstract

The cardinal secretary search problem confronts the decision maker with more or less candidates who have identically and independently distributed values and appear successively in a random order without recall of earlier candidates. Its benchmark solution implies monotonically decreasing sequences of optimal value aspirations (acceptance thresholds) for any number of remaining candidates. We compare experimentally observed aspirations with optimal ones for different numbers of (remaining) candidates and methods of experimental choice elicitation: “hot” collects play data, “warm” asks for an acceptance threshold before confronting the next candidate, and “cold” for a complete profile of trial-specific acceptance thresholds. The initially available number of candidates varies across elicitation methods to obtain more balanced data. We find that actual search differs from benchmark behavior, in average search length and success, but also in some puzzling qualitative aspects.