The ``less is more effect'' (LIME) occurs when a recognition-dependent agent has a greater probability of choosing the better item than a more knowledgeable agent who recognizes more items. Goldstein and Gigerenzer (2002) define alpha as the probability that a correct choice is made on the basis of recognition alone and beta the probability that a correct choice is made when both items are recognized (via additional cues). They claim that the LIME occurs only when alpha > beta (and assuming alpha > 1/2). However, their argument also assumes that alpha and beta remain constant as the number of recognized items, n, varies. In fact, it can be shown that neither of these parameters generally remains constant as n varies, and neither of them are simple functions of n. Therefore, a new theoretical basis for the LIME is needed. This paper provides mathematical results for understanding when the LIME can occur and elucidates implications of these results. The major findings presented here are as follows: * Demonstrations that the LIME can occur when alpha leq beta and fail to occur when alpha > beta, and derivation of the conditions for these co-occurrences; * A new characterization of the conditions under which the LIME occurs; * Generalizations of this characterization to handle imperfect recognition; and * Characterization of when the LIME occurs as more items become recognized. The primary implication of these results is that the advantage of the recognition cue depends not only on cue validities, but also on the order in which items are learned. This realization, in turn, suggests that research in this area should incorporate a more dynamic focus on learning and memory processes, and the effects of reputational information.
