Optimal categorization

The importance of categorical reasoning in human cognition is well-established in psychology and cognitive science, and one of the most important functions of categorization is to facilitate prediction. This paper provides a model of optimal categorization. In the beginning of each period a subject observes a two-dimensional object in one dimension and wants to predict the object’s value in the other dimension. The subject partitions the space of objects into categories. She has a data base of objects that were observed in both dimensions in the past. The subject determines what category the new object belongs to on the basis of observation of its …rst dimension. The subject predicts that its value in the second dimension will be equal to the average value among the past observations in the corresponding category. At the end of each period the second dimension is observed and the observation is stored in the data base. The main result is that the optimal number of categories is determined by a trade-o¤ between (a) decreasing the size of categories in order to enhance category homogeneity, and (b) increasing the size of categories in order to enhance category sample size. Keywords: Categorization; Priors; Prediction; Similarity-Based Reasoning. JEL codes: C72. Thanks to Jörgen Weibull for helpful advice. The paper has also bene…ted from comments by Philippe Jehiel, Topi Miettinen and Robert Östling, as well as participants at the Third Nordic Workshop in Behavioral and Experimental Economics in Copenhagen, November, 2008 and SUDSWEc in Uppsala, May 2009. Financial support from the Jan Wallander and Tom Hedelius Foundation is gratefully acknowledged. yE-mail: [email protected]. Mail: Department of Economics, Stockholm School of Economics, P.O. Box 6501, SE-113 83 Stockholm, Sweden.