Skip to main content
Journal of the Experimental Analysis of Behavior logoLink to Journal of the Experimental Analysis of Behavior
. 1984 Mar;41(2):183–192. doi: 10.1901/jeab.1984.41-183

Confirmation of linear system theory prediction: Changes in Herrnstein's k as a function of changes in reinforcer magnitude

J J McDowell, Helena M Wood
PMCID: PMC1348031  PMID: 16812366

Abstract

Eight human subjects pressed a lever on a range of variable-interval schedules for 0.25¢ to 35.0¢ per reinforcement. Herrnstein's hyperbola described seven of the eight subjects' response-rate data well. For all subjects, the y-asymptote of the hyperbola increased with increasing reinforcer magnitude and its reciprocal was a linear function of the reciprocal of reinforcer magnitude. These results confirm predictions made by linear system theory; they contradict formal properties of Herrnstein's account and of six other mathematical accounts of single-alternative responding.

Keywords: linear system theory, Herrnstein's equation, quantitative law of effect, choice, reinforcer magnitude, variable-interval schedules, lever press, humans

Full text

PDF
183

Selected References

These references are in PubMed. This may not be the complete list of references from this article.

  1. Bradshaw C. M., Szabadi E., Bevan P. Behavior of humans in variable-interval schedules of reinforcement. J Exp Anal Behav. 1976 Sep;26(2):135–141. doi: 10.1901/jeab.1976.26-135. [DOI] [PMC free article] [PubMed] [Google Scholar]
  2. Bradshaw C. M., Szabadi E., Bevan P. Relationship between response rate and reinforcement frequency in variable-interval schedules: the effect of the concentration of sucrose reinforcement. J Exp Anal Behav. 1978 May;29(3):447–452. doi: 10.1901/jeab.1978.29-447. [DOI] [PMC free article] [PubMed] [Google Scholar]
  3. Catania A. C. Self-inhibiting effects of reinforcement. J Exp Anal Behav. 1973 May;19(3):517–526. doi: 10.1901/jeab.1973.19-517. [DOI] [PMC free article] [PubMed] [Google Scholar]
  4. FLESHLER M., HOFFMAN H. S. A progression for generating variable-interval schedules. J Exp Anal Behav. 1962 Oct;5:529–530. doi: 10.1901/jeab.1962.5-529. [DOI] [PMC free article] [PubMed] [Google Scholar]
  5. 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]
  6. 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]
  7. Killeen P. R., Hanson S. J., Osborne S. R. Arousal: its genesis and manifestation as response rate. Psychol Rev. 1978 Nov;85(6):571–581. [PubMed] [Google Scholar]
  8. 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]
  9. McDowell J. J., Kessel R. A multivariate rate equation for variable-interval performance. J Exp Anal Behav. 1979 Mar;31(2):267–283. doi: 10.1901/jeab.1979.31-267. [DOI] [PMC free article] [PubMed] [Google Scholar]
  10. McDowell J. J., Sulzen H. M. Dynamic equilibrium on a cyclic-interval schedule with a ramp. J Exp Anal Behav. 1981 Jul;36(1):9–19. doi: 10.1901/jeab.1981.36-9. [DOI] [PMC free article] [PubMed] [Google Scholar]
  11. McDowell J. J. Wilkinson's method of estimating the parameters of Herrnstein's hyperbola. J Exp Anal Behav. 1981 May;35(3):413–414. doi: 10.1901/jeab.1981.35-413. [DOI] [PMC free article] [PubMed] [Google Scholar]
  12. 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]
  13. Rachlin H. A molar theory of reinforcement schedules. J Exp Anal Behav. 1978 Nov;30(3):345–360. doi: 10.1901/jeab.1978.30-345. [DOI] [PMC free article] [PubMed] [Google Scholar]
  14. Staddon J. E. On Herrnstein's equation and related forms. J Exp Anal Behav. 1977 Sep;28(2):163–170. doi: 10.1901/jeab.1977.28-163. [DOI] [PMC free article] [PubMed] [Google Scholar]
  15. Tryon W. W. A simplified time-series analysis for evaluating treatment interventions. J Appl Behav Anal. 1982 Fall;15(3):423–429. doi: 10.1901/jaba.1982.15-423. [DOI] [PMC free article] [PubMed] [Google Scholar]
  16. Williams B. A. Another look at contrast in multiple schedules. J Exp Anal Behav. 1983 Mar;39(2):345–384. doi: 10.1901/jeab.1983.39-345. [DOI] [PMC free article] [PubMed] [Google Scholar]

Articles from Journal of the Experimental Analysis of Behavior are provided here courtesy of Society for the Experimental Analysis of Behavior

RESOURCES