A Note on the Expected Number of Interviews When Talent is Uniformly Distributed
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Optimal stopping problems give rise to random distributions describing how many applicants the decision-maker will observe or interview before choosing one, a quantity sometimes referred to as the optimal stopping time. Despite the fact that is has important practical implications, this quantity is not widely studied. This short research note considers how many interviews are expected to be conducted when a decision-maker has to choose a candidate from a pool of sequential applicants with uniformly distributed talent and no recall, in the vein of previously studied Cayley-Moser and Secretary Problems. In terms of theoretical contribution, we derive algebraically the expected number of interviews when the decision-maker can only assess candidates using a rank-based indicator. In terms of empirical contribution, we show how the expected number of interviews relates to the size of the applicant pool when payoff values are observable. Finally, we present a new conjecture around the median number of interviews that will be conducted in the full-information setting.
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