THE DEPENDENCE OF p , ON f l IN GAMBLINO

By "simple situations" I mean those experimental designs commonly used in psychophysics, learning, and motivation, especially in studies intended to test one or another mathematical model. In fact, in this chapter only experiments for which the subject has two possible responses are discussed because mathematical theories are moderately well worked out only for these simple situations. Even there we still do not understand completely what is involved, as we shall see. If we examine existing mathematical theories for these simple situations, we find two quite different classes of models, which, when we focus on their mathematical structure, may be described as stochastic and static decomposition models or, when we focus on their psychological interpretations, as adaptive and analytic models. Current adaptive (or learning) models attempt to capture a subject's trial-by-trial choice behavior in terms of a stochastic process. These models apply to situations in which the same choice is repeatedly presented and the outcome to the subject on each trial depends both on his response and on the stimulus presented. The theoretical problem is to discover what remains invariant from trial to trial and, therefore, what constrains