Foundations Of Cognitive Science

Matching Law

A great deal of experimental evidence suggests that a variety of organisms are intuitive statisticians (Gallistel, 1990; Peterson & Beach, 1967; Shanks, 1995).  The matching law is a mathematical formalism that was originally used to explain variations in response frequency.  It states that the rate of a response reflects the rate of its obtained reinforcement.  For instance, if response A is reinforced twice as frequently as response B, then A will appear twice as frequently as B (Herrnstein, 1961).  The matching law also predicts how response strength varies with reinforcement frequency (de Villiers & Herrnstein, 1976).  A great deal of evidence has shown that the matching law governs many tasks in psychology and economics (Davison & McCarthy, 1988; de Villiers, 1977; Herrnstein, 1997).


  1. Davison, M., & McCarthy, D. (1988). The Matching Law : A Research Review. Hillsdale, N.J.: L. Erlbaum.
  2. de Villiers, P. (1977). Choice in concurrent schedules and a quantitative formulation of the law of effect. In W. K. Honig & J. E. R. Staddon (Eds.), Handbook of Operant Behavior (pp. 233-287). Englewood Cliffs, NJ: Prentice-Hall.
  3. de Villiers, P., & Herrnstein, R. J. (1976). Toward a law of response strength. Psychological Bulletin, 83(6), 1131-1153.
  4. Gallistel, C. R. (1990). The Organization Of Learning. Cambridge, MA: MIT Press.
  5. Herrnstein, R. J. (1961). Relative and absolute strength of response as a function of frequency of reinforcement. Journal of the Experimental Analysis of Behavior, 4(3), 267-272.
  6. Herrnstein, R. J. (1997). The Matching Law : Papers in Psychology and Economics. New York: Harvard University Press.
  7. Peterson, C. R., & Beach, L. R. (1967). Man as an intuitive statistician. Psychological Bulletin, 68(1), 29-46.
  8. Shanks, D. R. (1995). The Psychology Of Associative Learning. Cambridge, UK: Cambridge University Press.

(Added October 2010)