Analysis of strategy for the Secretary problem with cardinal function based on job specifications

Abstract

The classical Secretary problem is an applied mathematical model forchoosing the best applicant from a sample of a given size; the decider can not returnto an already rejected candidate and does not a priori know the scale of quality of thecandidates. In this well-known problem with a given number of data with unknowndistributions, we should stop the search once we consider a number to be the highestone. We opt for the original motivation, but rather than attempting to choose thebest one and fail in most cases, we suggest a strategy to control the mean value ofthe chosen one. The utility of the candidates in different experiments is designedbased on the theoretic distribution for specific job titles; we use a cardinal functionwith the argument being the candidate’s percentile among the population. Based onthe experiment, we present strategies for hiring for different roles and reveal that thestrategy has to be specific for a job; otherwise, it could be suboptimal.Our strategies are based on two parameters: the size of the sample part we examineand reject at the beginning of the search and the percentile from the examined samplewe demand the candidate to outperform to be accepted. We analysed all possibilitiesfor ordering 12 candidates and evaluated the strategies based on the experiment.