Abstract
Herrnstein's matching theory requires the parameter, k, which appears in the single-alternative form of the matching equation, to remain invariant with respect to changes in reinforcement parameters like magnitude or immediacy. Recent experiments have disconfirmed matching theory by showing that the invariant-k requirement does not hold. However, the theory can be asserted in a purely algebraic form that does not require an invariant k and that is not disconfirmed by the recent findings. In addition, both the original and the purely algebraic versions of matching theory can be asserted in forms that allow for commonly observed deviations from matching (bias, undermatching, and overmatching). The recent finding of a variable k does not disconfirm these versions of matching theory either. As a consequence, matching remains a viable theory of behavior, the strength of which lies in its general conceptualization of all behavior as choice, and in its unified mathematical treatment of single- and multialternative environments.
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Selected References
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- Baum W. M. Matching, undermatching, and overmatching in studies of choice. J Exp Anal Behav. 1979 Sep;32(2):269–281. doi: 10.1901/jeab.1979.32-269. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Baum W. M. On two types of deviation from the matching law: bias and undermatching. J Exp Anal Behav. 1974 Jul;22(1):231–242. doi: 10.1901/jeab.1974.22-231. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Davison M. C., Hunter I. W. Performance on variable-interval schedules arranged singly and concurrently. J Exp Anal Behav. 1976 May;25(3):335–345. doi: 10.1901/jeab.1976.25-335. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Herrnstein R. J. Formal properties of the matching law. J Exp Anal Behav. 1974 Jan;21(1):159–164. doi: 10.1901/jeab.1974.21-159. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Herrnstein R. J. On the law of effect. J Exp Anal Behav. 1970 Mar;13(2):243–266. doi: 10.1901/jeab.1970.13-243. [DOI] [PMC free article] [PubMed] [Google Scholar]
- McDowell J. J. An analytic comparison of Herrnstein's equations and a multivariate rate equation. J Exp Anal Behav. 1980 May;33(3):397–408. doi: 10.1901/jeab.1980.33-397. [DOI] [PMC free article] [PubMed] [Google Scholar]
- McDowell J. J. The importance of Herrnstein's mathematical statement of the law of effect for behavior therapy. Am Psychol. 1982 Jul;37(7):771–779. doi: 10.1037//0003-066x.37.7.771. [DOI] [PubMed] [Google Scholar]
- McDowell J. J., Wood H. M. Confirmation of linear system theory prediction: Changes in Herrnstein's k as a function of changes in reinforcer magnitude. J Exp Anal Behav. 1984 Mar;41(2):183–192. doi: 10.1901/jeab.1984.41-183. [DOI] [PMC free article] [PubMed] [Google Scholar]
- McDowell J. J., Wood H. M. Confirmation of linear system theory prediction: Rate of change of Herrnstein's kappa as a function of response-force requirement. J Exp Anal Behav. 1985 Jan;43(1):61–73. doi: 10.1901/jeab.1985.43-61. [DOI] [PMC free article] [PubMed] [Google Scholar]
- McLean A. P., White K. G. Temporal constraint on choice: Sensitivity and bias in multiple schedules. J Exp Anal Behav. 1983 May;39(3):405–426. doi: 10.1901/jeab.1983.39-405. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Rachlin H. On the tautology of the matching law. J Exp Anal Behav. 1971 Mar;15(2):249–251. doi: 10.1901/jeab.1971.15-249. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Staddon J. E. Spaced responding and choice: a preliminary analysis. J Exp Anal Behav. 1968 Nov;11(6):669–682. doi: 10.1901/jeab.1968.11-669. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Wearden J. H., Burgess I. S. Matching since Baum (1979). J Exp Anal Behav. 1982 Nov;38(3):339–348. doi: 10.1901/jeab.1982.38-339. [DOI] [PMC free article] [PubMed] [Google Scholar]