386 Conditioning and Learning
Figure 13.4 Hyperbolic discounting function. This figure shows how the value of a re-
ward (in arbitrary units) decreases as a function of delay according to the Mazur’s (1984)
hyperbolic-decay model (Equation 13.6, with K=0.2).matching law, and they are integrative in the sense that they
provide a quantitative description of data from a variety of
choice procedures. Determining the optimal choice model
may have important implications for a variety of issues, in-
cluding how conditioned value is influenced by parameters of
reinforcement, as well as the nature of the temporal discount-
ing function.
Grace (1994, 1996) showed how the temporal context ef-
fects predicted by Fantino’s delay-reduction theory could be
incorporated in an extension of the generalized matching law.
His contextual choice model can describe choice in concur-
rent schedules, concurrent chains, and the adjusting-delay
procedure, on average accounting for over 90% of the vari-
ance in data from these procedures. The success of Grace’s
model as applied to the nonhuman-choice data suggests that
temporal discounting may be best described in terms of a
model with a power function component; moreover, such a
model accounts for representative human data at least as well
as the hyperbolic-decay model does (Grace, 1999). However,
Mazur (2001) has recently proposed an alternative model
based on the hyperbolic-decay model. Mazur’s hyperbolic
value-addition model is based on a principle similar to delay-
reduction theory, and it provides an account of the data of
comparable accuracy to that of Grace’s model. Future re-
search will determine which of these models (or whether an
entirely different model) provides the best overall account of
behavioral choice and temporal discounting.
Resistance to Change: An Alternative View
of Response Strength
Although response rate has long been considered the standard
measure of the strength of an instrumental response, it is not
without potential problems. Response strength represents the
product of the conditioning process. In terms of the law of ef-
fect, it should vary directly with parameters that correspond to
intuitive notions of hedonic value. For example, response
strength should be a positive function of reinforcement mag-
nitude. However, studies have found that response rate often
decreases with increases in magnitude (Bonem & Crossman,
1988). In light of this and other difficulties, researchers have
sought other measures of response strength that are more con-
sistently related to intuitive parameters of reinforcement.
One such alternative measure is resistance to change.
Nevin (1974) conducted several experiments in which pi-
geons responded in multiple schedules. After baseline train-
ing, he disrupted responding in both components by either
home-cage prefeeding or extinction. He found that respond-
ing in the component that provided the relatively richer
reinforcement—in terms of greater rate, magnitude, or imme-
diacy of reinforcement—decreased less compared with base-
line responding for that component than did responding in the
leaner component. Based on these results and others, Nevin
and his colleagues have proposed behavioral momentum the-
ory,which holds that resistance to change and response rate
are independent aspects of behavior analogous to mass and
velocity in classical physics (Nevin, Mandell, & Atak, 1983).
According to this theory, reinforcement increases a mass-like
aspect of behavior which can be measured as resistance to
change.
From a procedural standpoint, the components in multiple
schedules resemble terminal links in concurrent chains be-
cause differential conditions of reinforcement are signaled by
distinctive stimuli and are available successively. Moreover,
the same variables (e.g., reinforcement rate, magnitude, and
immediacy) that increase resistance to change also increase