In the Sequential Selection Problem (SSP), immediate and irrevocable decisions need to be made while candidates from a finite set are being examined one-by-one. The goal is to assign a limited number of @math available jobs to the best possible candidates. Standard SSP variants begin with an empty selection set (cold-starting) and perform the selection process once (single-round), over a single candidate set. In this paper we introduce the Multi-round Sequential Selection Problem (MSSP) which launches a new round of sequential selection each time a new set of candidates becomes available. Each new round has at hand the output of the previous one, i.e. its @math selected employees, and tries to update optimally that selection by reassigning each job at most once. Our setting allows changes to take place between two subsequent selection rounds: resignations of previously selected subjects or and alterations of the quality score across the population. The challenge for a selection strategy is thus to efficiently adapt to such changes. For this novel problem we adopt a cutoff-based approach, where a precise number of candidates should be rejected first before starting to select. We set a rank-based objective of the process over the final job-to-employee assignment and we investigate analytically the optimal cutoff values with respect to the important parameters of the problem. Finally, we present experimental results that compare the efficiency of different selection strategies, as well as their convergence rates towards the optimal solution in the case of stationary score distributions.
A very limited number of papers study algorithmic notions related to repeated selections @cite_5 , as well as the human capacity to learn the right cutoff after reviewing multiple independent candidate sets @cite_3 @cite_22 . However, @cite_5 develops a non cutoff-based strategy and is implemented regarding two distinct aims: to maximize the probability of selecting the best, or to maximize the expected score of the selected . Its conclusion states that learning the score distribution does contribute to the efficiency of the selection only the second aim. An experimental comparison of simpler and intuitive non cutoff-based heuristics is provided in @cite_24 . More sophisticated adaptive strategies worth mentioning are the @cite_6 and the work in @cite_18 . A rather different scenario concerns a startup company (or a new ambitious business unit) which is initially funded by a handful of people but is about to grow larger. The so-called @cite_8 refers to the process that aims at driving the optimal growth of personnel using an adaptive selection threshold based on the already employed individuals. Among heuristics, such as hiring above the worst or best employees, hiring above the mean employee score shown to be the best performing strategy.
@cite_18 @cite_22 @cite_8 @cite_3 @cite_6 @cite_24 @cite_5
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We introduce the hiring problem, in which a growing company continuously interviews and decides whether to hire applicants. This problem is similar in spirit but quite different from the well-studied secretary problem. Like the secretary problem, it captures fundamental aspects of decision making under uncertainty and has many possible applications. We analyze natural strategies of hiring above the current average, considering both the mean and the median averages; we call these Lake Wobegon strategies. Like the hiring problem itself, our strategies are intuitive, simple to describe, and amenable to mathematically and economically significant modifications. We demonstrate several intriguing behaviors of the two strategies. Specifically, we show dramatic differences between hiring above the mean and above the median. We also show that both strategies are intrinsically connected to the lognormal distribution, leading to only very weak concentration results, and the marked importance of the first few hires on the overall outcome. In the classical secretary problem, one attempts to find the maximum of an unknown and unlearnable distribution through sequential search. In many real-world searches, however, distributions are not entirely unknown and can be learned through experience. To investigate learning in such a repeated secretary problem we conduct a large-scale behavioral experiment in which people search repeatedly from fixed distributions. In contrast to prior investigations that find no evidence for learning in the classical scenario, in the repeated setting we observe substantial learning resulting in near-optimal stopping behavior. We conduct a Bayesian comparison of multiple behavioral models which shows that participants' behavior is best described by a class of threshold-based models that contains the theoretically optimal strategy. In fact, fitting such a threshold-based model to data reveals players' estimated thresholds to be surprisingly close to the optimal thresholds after only a small number of games. The objective of this paper is to present two theorems which are directly applicable to optimal stopping problems involving independent indicator functions. The proofs are elementary. One implication of the results is a convenient solution algorithm to obtain the optimal stopping rule and the value. We will apply it to several examples of sequences of independent indicators, including sequences of random length. Another interesting implication of the results is that the well-known asymptotic value 1 e for the classical best-choice problem is in fact a typical lower bound in a much more general class of problems. Abstract The "secretary problem" models a class of optimal stopping decision tasks in which the binary decision to either stop or continue the search only depends on relative ranks. We present this problem in a computer-controlled experiment designed to investigate sequential observation and selection behavior in the context of employer hiring decisions. Our principal objectives are to test the descriptive power of the optimal decision policy; characterize and competitively test simple decision rules, or heuristics, that individuals might use in optimal stopping decision tasks; and examine the sensitivity of the various decision rules by computer simulation. Our simulation results show that the optimal policy is insensitive to moderate deviations from the optimal cutoff value, and that a simple, non-optimal decision rule that counts the number of successive non-candidates performs remarkably well. Model comparisons show that simple cutoff decision rules account for the decisions of the majority of the subjects. The observed tendency to stop the search too early is accounted for by postulating an endogenous cost of time spent in the search. Abstract Consideration is given to an extension of the so-called secretary problem in which each alternative has an observable value drawn from a distribution unknown a priori. A uniform distribution is considered here, because this gives analytical solutions which are easily compared with previous work. It is shown that when maximizing the probability of selecting the best candidate, learning does not contribute to the solution. When maximizing expected value, learning does play a role, giving a solution intermediate between that based on ranks and that based on known distributions.