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Effects of adding a second reinforcement alternative: Implications for
Herrnstein’s interpretation of <i>r</i><abbr><sub><i>e</i></sub></abbr> .
Soto, P. L., McDowell, J. J, & Dallery, J. (2005).
Effects of adding a second reinforcement alternative: Implications for
Herrnstein’s interpretation of re .
Journal of the Experimental Analysis of Behavior, 84, 185-225.
Herrnstein’s hyperbola describes the relation between response rate and
reinforcer rate on variable-interval (VI) schedules. According to Herrnstein’s
(1970) interpretation, the parameter re
represents the reinforcer rate
extraneous to the alternative to which the equation is fitted (the target
alternative). The hyperbola is based on an assumption that extraneous
reinforcer rate remains constant with changes in reinforcer rate on the target
alternative (the constant-re assumption)
and that matching with no bias and
perfect sensitivity occurs between response and reinforcer ratios. In the
present experiment, 12 rats pressed levers for food on a series of 10 VI
schedules arranged on the target alternative. Across conditions, six VI values
and extinction were arranged on a second alternative. Reinforcer rate on the
second alternative, r2, negatively
covaried with reinforcer rate on the target
alternative for five of the six VI values on the second alternative, and
significant degrees of bias and undermatching occurred in response ratios.
Given covariation of reinforcer rate on the second and target alternatives, the
constant-re assumption can be
maintained only by assuming that reinforcer rate
from unmeasured background sources, rb ,
covaries with reinforcer rate on the
second alternative such that their sum, re ,
remains constant. In a single-schedule arrangement, however,
re equals
rb and thus
rb is assumed to remain
constant, forcing a conceptual inconsistency between single- and concurrent-schedule
arrangements. Furthermore, although an alternative formulation of the
hyperbola can account for variations in bias and sensitivity, the modified
equation also is based on the constant-re
assumption and therefore suffers from
the same logical problem as the hyperbola when reinforcer rate on the second
alternative covaries with reinforcer rate on the target alternative.
Key words: Herrnstein’s hyperbola, matching theory, extraneous reinforcer rate,
concurrent VI schedules, lever pressing, rats