Optimal Strategies for Personnel Selection When Candidates Can Reject Offers

Imagine that you have five managerial positions to fill. Your procedures for hiring involve extensive interviewing of prospective candidates, and this is a costly procedure-both in terms of actual money and the time spent in interviews. From your experience, you feel that your interviewing procedures are fairly diagnostic of subsequent job success, although mistakes have been made in the past. The first question that arises concerns the decision of the number of people to be screened for the vacant positions. This is the problem we address in this paper-a problem which, as will be illustrated below, leads to a consideration of most of the important issues in the personnel selection process. For instance, experience may indicate that there is severe competition for good people, so that there is a fair chance that certain candidates will not accept job offers. However, there are a number of strategies that could be used to increase the probability that good candidates accept your offer. For example, jobs could be offered on the spot, more money could be offered, etc. If more rewards are to be offered, however, the question arises as to how much one should be willing to pay to increase the probability of acceptance to any desired level. To answer these questions, a decision-theoretic approach is used. This approach was first suggested in a personnel context in the classic monograph of Cronbach and Gleser.1 While we owe much to their work, our major interest lies in problems they did not fully explore and, in particular, optimal strategies when the candidates can reject job offers. This constraint seems so important to us that it is surprising that more research has not been devoted to it.2 The end product of the present study is a simple interactive computer