A theory of cutoff formation under imperfect information
Numerous models in the Management Science literature contain constructions that are a variant of the following: A decision-maker must choose from a set of alternatives based on imperfect information as to their relative quality, while further evaluation, though costly, provides more accurate information. We examine decision heuristics in which the optimal search policy entails a screening strategy limiting the number of alternatives in the subsequent, costly evaluation. There are two general methods for accomplishing this screening: Quota cutoffs operate by selecting the optimal number of alternatives to evaluate; Level cutoffs operate by specifying a minimally-acceptable level of the imperfect screening indicator. The present paper has three main objectives. First, to define the Level and Quota cutoff methods, broadly characterize optimal behavior for each and determine what aspects of the decision environment predispose one to be superior to the other; second, to introduce the concomitants of order statistics as a methodology for exploring decision problems when information is imperfectly known; and third, to discuss the pivotal role of default, or fallback, options in a broad class of search problems. Quota and Level strategies restrict the number of alternatives passing the cutoff-based screen. Because restrictive cutoffs reduce evaluation costs while lowering the expected quality of the item finally selected, changes in the decision environment making the evaluation process less beneficial or increasing its cost drive the optimal cutoff to be more restrictive. In particular, increases in unit evaluation cost, improvement in the quality of a fallback option, decreases in the total number of alternatives available or improvement in the precision of the final evaluation process all lead to more restrictive cutoffs at optimum. These results hold over a remarkably broad range of assumptions and conditions. We also find that a better screening indicator leads to more restrictive screening when evaluation costs are low but, surprisingly, to less restrictive screening when costs are high. Comparing the two strategies, we find the unexpected result that the Quota cutoff strategy is generally superior to the Level, except under one of two fairly uncommon sets of circumstances: when evaluation cost is prohibitively high, or when there is a fallback option of very high quality.
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