Non-maximal performance in probabilistic categorization.
Lindsay M. Oliver · Deep Blue (University of Michigan) · 1995
When faced with categorization tasks that do not allow for complete accuracy, people frequently fail to attain the maximal possible accuracy. This study investigates three models of probabilistic categorization, and examines the assumptions of each regarding non-maximal performance. Each model predicts non-maximal responding in probabilistic categorization tasks, but rests on very different assumptions regarding the source of the non-maximality. The first of the three models, General Recognition Theory (GRT) (Ashby & Maddox, 1990) assumes that category exemplars are represented as points in multidimensional space. During categorization people are assumed to use decision bounds which divide perceptual space into response regions. It is assumed that people use the maximal decision bound deterministically. Failures to perfectly apply the maximal decision bound are assumed to be due to noise. The Micromatching Hypothesis (MH) (Lee, 1963, 1968) assumes that categorization decisions are based on the relative frequency of each category. The probability of making a Category A response to a given stimulus is equal to the proportion of times the stimulus has occurred as a member of Category A. Under the MH, non-maximal performance is a byproduct of a probabilistic response rule. Finally, the Mixture Model (MM) assumes that people construct a set of response strategies. For each categorization decision a single strategy is applied and tested against information received from the categorization situation. Under the Mixture Model, people respond with a mixture of maximal and alternate strategies that result in less than maximal performance. This study assesses the predictions of each model in tasks that vary the degree of overlap between two normally distributed categories. When the degree of overlap between two normally distributed categories is varied, each model makes quantitatively or qualitatively distinct predictions in terms of the degree of deviation from maximal found in the ratio of Category A responses to Category B responses. The data reported here do not support any of the models but can be accommodated by a modification of the Mixture Model.