pmc logo image
Logo of jeabehavJournal of the Experimental Analysis of Behavior Web SiteSubscriber LoginJournal of Applied Behavior Analysis Web SiteSubscription InformationInformation for AuthorsJournal of the Experimental Analysis of Behavior Web SiteJournal of the Experimental Analysis of Behavior Web Site

Formats:

J Exp Anal Behav. 1974 July; 22(1): 231–242.
doi: 10.1901/jeab.1974.22-231.
PMCID: PMC1333261
On two types of deviation from the matching law: bias and undermatching1
William M. Baum
1The new research reported and the preparation of this paper were supported by grants from the National Science Foundation and the National Institutes of Health to Harvard University. Reprints may be obtained from the author, Department of Psychology, William James Hall, Harvard University, Cambridge, Mass. 02138.
Abstract
Data on choice generally conform closely to an equation of the form: log(B1/B2)=a log(r1/r2+log k, where B1 and B2 are the frequencies of responding at Alternatives 1 and 2, r1 and r2 are the obtained reinforcement from Alternatives 1 and 2, and a and k are empirical constants. When a and k equal one, this equation is equivalent to the matching relation: B1/B2=r1/r2. Two types of deviation from matching can occur with this formulation: a and k not equal to one. In some experiments, a systematically falls short of one. This deviation is undermatching. The reasons for undermatching are obscure at present. Some evidence suggests, however, that factors favoring discrimination also favor matching. Matching (a=1) may represent the norm in choice when discrimination is maximal. When k differs from one, its magnitude indicates the degree of bias in choice. The generalized matching law predicts that bias should take this form (adding a constant proportion of responding to the favored alternative). Data from a variety of experiments indicate that it generally does.
Full text
Full text is available as a scanned copy of the original print version. Get a printable copy (PDF file) of the complete article (1.4M), or click on a page image below to browse page by page. Links to PubMed are also available for Selected References.
Selected References
These references are in PubMed. This may not be the complete list of references from this article.
  • Baum William M. Time allocation and negative reinforcement. J Exp Anal Behav. 1973 Nov;20(3):313–322. [PubMed]
  • Baum William M, Rachlin Howard C. Choice as time allocation. J Exp Anal Behav. 1969 Nov;12(6):861–874. [PubMed]
  • Brownstein Aaron J, Pliskoff Stanley S. Some effects of relative reinforcement rate and changeover delay in response-independent concurrent schedules of reinforcement. J Exp Anal Behav. 1968 Nov;11(6):683–688. [PubMed]
  • Fantino Edmund, Squires Nancy, Delbrück Nicola, Peterson Christa. Choice behavior and the accessibility of the reinforcer. J Exp Anal Behav. 1972 Jul;18(1):35–43. [PubMed]
  • Findley JD. Preference and Switching under Concurrent Scheduling. J Exp Anal Behav. 1958 Apr;1(2):123–144. [PubMed]
  • HERRNSTEIN RJ. Relative and absolute strength of response as a function of frequency of reinforcement. J Exp Anal Behav. 1961 Jul;4:267–272. [PubMed]
  • Herrnstein RJ. On the law of effect. J Exp Anal Behav. 1970 Mar;13(2):243–266. [PubMed]
  • Hollard Valerie, Davison MC. Preference for qualitatively different reinforcers. J Exp Anal Behav. 1971 Nov;16(3):375–380. [PubMed]
  • Killeen Peter. A yoked-chamber comparison of concurrent and multiple schedules. J Exp Anal Behav. 1972 Jul;18(1):13–22. [PubMed]
  • Killeen Peter. The matching law. J Exp Anal Behav. 1972 May;17(3):489–495. [PubMed]
  • Labounty Charles E, Reynolds GS. An analysis of response and time matching to reinforcement in concurrent ratio-interval schedules. J Exp Anal Behav. 1973 Jan;19(1):155–166. [PubMed]
  • Lander DG, Irwin RJ. Multiple schedules: effects of the distribution of reinforcements between component on the distribution of responses between conponents. J Exp Anal Behav. 1968 Sep;11(5):517–524. [PubMed]
  • Nevin John A. Rates and patterns of responding with concurrent fixed-interval and variable-interval reinforcement. J Exp Anal Behav. 1971 Sep;16(2):241–247. [PubMed]
  • Rachlin Howard. On the tautology of the matching law. J Exp Anal Behav. 1971 Mar;15(2):249–251. [PubMed]
  • REYNOLDS GS. On some determinants of choice in pigeons. J Exp Anal Behav. 1963 Jan;6:53–59. [PubMed]
  • Shimp Charles P, Wheatley Kimbal L. Matching to relative reinforcement frequency in multiple schedules with a short component duration. J Exp Anal Behav. 1971 Mar;15(2):205–210. [PubMed]
  • Shull RL, Pliskoff SS. Changeover delay and concurrent schedules: some effects on relative performance measures. J Exp Anal Behav. 1967 Nov;10(6):517–527. [PubMed]
  • Staddon JER. Spaced responding and choice: a preliminary analysis. J Exp Anal Behav. 1968 Nov;11(6):669–682. [PubMed]
  • STEVENS SS. On the psychophysical law. Psychol Rev. 1957 May;64(3):153–181. [PubMed]
  • Stubbs D Alan, Pliskoff Stanley S. Concurrent responding with fixed relative rate of reinforcement. J Exp Anal Behav. 1969 Nov;12(6):887–895. [PubMed]
  • Todorov João Claudio. Component duration and relative response rates in multiple schedules. J Exp Anal Behav. 1972 Jan;17(1):45–49. [PubMed]
  • Trevett AJ, Davison MC, Williams RJ. Performance in concurrent interval schedules. J Exp Anal Behav. 1972 May;17(3):369–374. [PubMed]