How to Find the One - Secretary Problem Extended with Uncertain Observations

Abstract

Making a good decision is often a challenge. How to choose your ideal house? How to find your true love? These problems resemble the mathematical puzzle called the secretary problem. In the classic secretary problem, administrators want to hire the best secretary from n applicants. The secretaries present themselves one by one. Each decision, rejecting or accepting, needs to be immediate, is permanent, but can only be based on the ranking of seen applicants. Who should they hire? The optimal strategy is a cut-off strategy, where the number of applicants one needs to wait is n/e, with n is the number of applicants, which is approximately 37 with n = 100. After 37%, the administrators should hire the first who is better than all they have seen before. In this study, the effect of uncertain observations on the chance of success of cut-off strategies has been evaluated by the use of computer simulations. Computer simulations were used to simulate versions of the secretary problem with intervals, normal distributions and pareto distributions. The trend showed that the larger the uncertainty, the lower the cutoffpoint from the optimal strategy. The reserved advice is: if you are not sure, choose sooner!