The importance of Herrnstein's mathematical statement of the law of effect for behavior therapy.

Herrnstein's mathematical statement of the law of effect improves on Skinner's view of rein- forcement by asserting (a) that response rate varies hy- perbolically with reinforcement rate and (b) that re- sponding is governed not only by reinforcement obtained for responding but also by reinforcement obtained from all other concurrent sources. Data from infrahuman organisms and from humans in laboratory and clinical situations support this new view of reinforcement. Clin- ically, Herrnstein's equation requires a broader envi- ronmental approach to conceptualizi ng cases and to applying reinforcement principles in therapy. The equation can help clinicians design treatment regimens more efficiently, and it suggests four new intervention strategies that may be especially useful in difficult cases, for example, when standard procedures are contra- indicated or in environments that already supply large amounts of reinforcement. During the past two decades, research in basic behavioral science has become increasingly con- cerned with formal, that is, mathematical, descrip- tions of behavior. Very recently, a number of fairly complete formalisms have been proposed that ac- count remarkably well for certain features of be- havior under specific environmental conditions (e.g., Killeen, 1979; McDowell & Kessel, 1979; Myerson & Miezin, 1980; Rachlin & Burkhard, 1978). The impetus for much of this work was the empirical success of Herrnstein's (1970) mathe- matical statement of the law of effect. It is not difficult to find cases in the history of science where a mathematical treatment has led to a substantially improved, and sometimes radi- cally different, understanding of the phenomenon it was meant to describe. The so-called Merton relation1 in medieval kinematics, for example, was ultimately responsible for laying to rest the Aris- totelian doctrine that motion, like color, was an inherent property of a body (Pedersen & Pihl, 1974). In a similar, although perhaps less radical, way Herrnstein's equation has led to an improved understanding of the effects of reinforcement on the behavior of organisms. The new view of reinforcement provided by Herrnstein's equation is especially important for contemporary behavior therapy, which relies on reinforcement principles for many of its tech- niques. This article will explain Herrnstein's math- ematical statement of the law of effect and ex- amine its importance for clinical practice. The basic features of the equation will be presented in the first section, followed by a brief review of con- firming evidence, with special attention paid to data from human subjects. In the second section, the clinical relevance of the equation will be dis- cussed.