Sequential selections with minimization of failure

Abstract

The decision-maker (DM) sequentially evaluates up to $N$ of different, rankable options. DM must select exactly the best one at the moment of its appearance. In the process of searching, DM finds out with each applicant whether she is the best applicant among those assessed so far (we call him a candidate). DM cannot return to rejected candidates. We discuss the psychological aspects of this selection problem, known in the literature as the secretary problem. The analysis is based on knowledge of the chances, and a subjective assessment of acceptance of the positive and negative effects DM’s decision. The acceptance assessment of success and failure is presented on subjective scales. We set an optimal policy that recommends analyzing applicants up to a certain point in time (a threshold time) without selecting any of them and then selecting the next encountered candidate. The determined optimal threshold depends on the level of acceptance of the positive and negative effects of the choice. This issue is discussed in the article.