Skip to main content
PMC home page
Journal of the Experimental Analysis of Behavior logoLink to Journal of the Experimental Analysis of Behavior
. 2000 Jan;73(1):23–43. doi: 10.1901/jeab.2000.73-23

Falsification of matching theory's account of single-alternative responding: Herrnstein's k varies with sucrose concentration.

J Dallery 1, J J McDowell 1, J S Lancaster 1
PMCID: PMC1284760  PMID: 10682338

Abstract

Eight rats pressed levers for varying concentrations of sucrose in water under eight variable-interval schedules that specified a wide range of reinforcement rate. Herrnstein's (1970) hyperbolic equation described the relation between reinforcement and responding well. Although the y asymptote, k, of the hyperbola appeared roughly constant over conditions that approximated conditions used by Heyman and Monaghan (1994), k varied when lower concentration solutions were included. Advances in matching theory that reflect asymmetries between response alternatives and insensitive responding were incorporated into Herrnstein's equation. After fitting the modified equation to the data, Herrnstein's k also increased. The results suggest that variation in k can be detected under a sufficiently wide range of reinforcer magnitudes, and they also suggest that matching theory's account of response strength is false. The results support qualitative predictions made by linear system theory.

Full Text

The Full Text of this article is available as a PDF (196.9 KB).

Selected References

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

  1. 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]
  2. 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]
  3. Bradshaw C. M., Ruddle H. V., Szabadi E. Relationship between response rate and reinforcement frequency in variable-interval schedules: II. Effect of the volume of sucrose reinforcement. J Exp Anal Behav. 1981 May;35(3):263–269. doi: 10.1901/jeab.1981.35-263. [DOI] [PMC free article] [PubMed] [Google Scholar]
  4. 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]
  5. 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]
  6. GUTTMAN N. Equal-reinforcement values for sucrose and glucose solutions compared with equal-sweetness values. J Comp Physiol Psychol. 1954 Oct;47(5):358–361. doi: 10.1037/h0062710. [DOI] [PubMed] [Google Scholar]
  7. HERRNSTEIN R. J. Relative and absolute strength of response as a function of frequency of reinforcement. J Exp Anal Behav. 1961 Jul;4:267–272. doi: 10.1901/jeab.1961.4-267. [DOI] [PMC free article] [PubMed] [Google Scholar]
  8. 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]
  9. 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]
  10. Heyman G. M., Monaghan M. M. Reinforcer magnitude (sucrose concentration) and the matching law theory of response strength. J Exp Anal Behav. 1994 May;61(3):505–516. doi: 10.1901/jeab.1994.61-505. [DOI] [PMC free article] [PubMed] [Google Scholar]
  11. KEESEY R. E. DURATION OF STIMULATION AND THE REWARD PROPERTIES OF HYPOTHALAMIC STIMULATION. J Comp Physiol Psychol. 1964 Oct;58:201–207. doi: 10.1037/h0043134. [DOI] [PubMed] [Google Scholar]
  12. KEESEY R. E., KLING J. W. Amount of reinforcement and free-operant responding. J Exp Anal Behav. 1961 Apr;4:125–132. doi: 10.1901/jeab.1961.4-125. [DOI] [PMC free article] [PubMed] [Google Scholar]
  13. KEESEY R. E. The relation between pulse frequency, intensity, and duration and the rate of responding for intracranial stimulation. J Comp Physiol Psychol. 1962 Oct;55:671–678. doi: 10.1037/h0049222. [DOI] [PubMed] [Google Scholar]
  14. KRAELING D. Analysis of amount of reward as a variable in learning. J Comp Physiol Psychol. 1961 Oct;54:560–565. doi: 10.1037/h0040833. [DOI] [PubMed] [Google Scholar]
  15. 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]
  16. McDowell J. J., Dallery J. Falsification of matching theory: changes in the asymptote of Herrnstein's hyperbola as a function of water deprivation. J Exp Anal Behav. 1999 Sep;72(2):251–268. doi: 10.1901/jeab.1999.72-251. [DOI] [PMC free article] [PubMed] [Google Scholar]
  17. 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]
  18. McDowell J. J. On the falsifiability of matching theory. J Exp Anal Behav. 1986 Jan;45(1):63–74. doi: 10.1901/jeab.1986.45-63. [DOI] [PMC free article] [PubMed] [Google Scholar]
  19. 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]
  20. 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]
  21. 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]
  22. Miller H. L. Matching-based hedonic scaling in the pigeon. J Exp Anal Behav. 1976 Nov;26(3):335–347. doi: 10.1901/jeab.1976.26-335. [DOI] [PMC free article] [PubMed] [Google Scholar]
  23. Ploog B. O., Zeigler H. P. Effects of food-pellet size on rate, latency, and topography of autoshaped key pecks and gapes in pigeons. J Exp Anal Behav. 1996 Jan;65(1):21–35. doi: 10.1901/jeab.1996.65-21. [DOI] [PMC free article] [PubMed] [Google Scholar]
  24. Ploog B. O., Zeigler H. P. Key-peck probability and topography in a concurrent variable-interval variable-interval schedule with food and water reinforcers. J Exp Anal Behav. 1997 Jan;67(1):109–129. doi: 10.1901/jeab.1997.67-109. [DOI] [PMC free article] [PubMed] [Google Scholar]
  25. Warren-Boulton F. R., Silberberg A., Gray M., Ollom R. Reanalysis of the equation for simple action. J Exp Anal Behav. 1985 Mar;43(2):265–277. doi: 10.1901/jeab.1985.43-265. [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