Wills, A. J., Reimers, S., Stewart, N., Suret, M., & McLaren I. P. L. (2000). Tests of the ratio rule in categorization. Quarterly Journal of Experimental Psychology, 53A, 983-1011.

Many theories of learning and memory (e.g., connectionist, associative, rational, exemplar based) produce psychological magnitude terms as output (i.e., numbers representing the momentary level of some subjective property). Many theories assume that these numbers may be translated into choice probabilities via the ratio rule, also known as the choice axiom (Luce, 1959) or the constant-ratio rule (Clarke, 1957). We present two categorization experiments employing artificial, visual, prototype-structured stimuli constructed from 12 symbols positioned on a grid. The ratio rule is shown to be incorrect for these experiments, given the assumption that the magnitude terms for each category are univariate functions of the number of category-appropriate symbols contained in the presented stimulus. A connectionist winner-take-all model of categorical decision (Wills & McLaren, 1997) is shown to account for our data given the same assumption. The central feature underlying the success of this model is the assumption that categorical decisions are based on a Thurstonian choice process (Thurstone, 1927, Case V) whose noise distribution is not double exponential in form.

Clarke, F. R. (1957). Constant-ratio rule for confusion matrices in speech communication. Journal of the Acoustical Society of America, 29, 715-720.

Luce, R. D. (1959). Individual choice behavior. New York: John Wiley & Sons.

Thurstone, L. L. (1927). A law of comparative judgment. Psychological Review, 34, 273-286.

Wills, A. J., & McLaren, I. P. L. (1997). Generalization in human category learning: A connectionist explanation of differences in generalization gradient after discriminative and non-discriminative training. Quarterly Journal of Experimental Psychology, 50A, 607-630.