A THEORY OF CUTOFF FORMATION UNDER IMPERFECT INFORMATION

Numerous models in the Management Science literature contain construct ions 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 m ore 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 g eneral methods for accomplishing this screening: Quota cutoffs operate by selecting the optimal number of alternatives to evaluate; Level cu toffs operate by specifying a minimally-acceptable level of the imperf ect screening indicator. The present paper has three main objectives. First, to define the Level and Quota cutoff methods, broadly character ize optimal behavior for each and determine what aspects of the decisi on environment predispose one to be superior to the other; second, to introduce the concomitants of order statistics as a methodology for ex ploring decision problems when information is imperfectly known; and t hird, 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 re strictive cutoffs reduce evaluation costs while lowering the expected quality of the item finally selected, changes in the decision environm ent making the evaluation process less beneficial or increasing its co st drive the optimal cutoff to be more restrictive. In particular, inc reases in unit evaluation cost, improvement in the quality of a fallba ck 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 rema rkably broad range of assumptions and conditions. We also find that a better screening indicator leads to more restrictive screening when ev aluation costs are low but, surprisingly, to less restrictive screenin g when costs are high. Comparing the two strategies, we find the unexp ected result that the Quota cutoff strategy is generally superior to t he Level, except under one of two fairly uncommon sets of circumstance s: when evaluation cost is prohibitively high, or when there is a fall back option of very high quality.