BEHAVIORISMMatching implies that an increase of 10 percent
(e.g., from 50 to 60 percent) in relative rate of
reinforcement for one alternative results in a simi-
lar increase in relative rate of response. In many
cases, the increase in relative rate of response is
less than expected (e.g., only 5 percent). This
failure to discriminate changes in relative rate of
reinforcement is incorporated within the theory
of generalized matching. To illustrate, low sensi-
tivity to changes in rate of reinforcement may
occur when an air-traffic controller rapidly switch-
es between two (or more) radar screens. As rela-
tive rate of targets increases on one screen, relative
rate of detection may be slow to change. General-
ized matching theory allows behaviorists to meas-
ure the degree of sensitivity and suggests proce-
dures to modify it (e.g., setting a minimal amount
of time on a screen before targets can be detected).
Matching theory is an important contribution
of modern behaviorism. In contrast to theories of
rational choice proposed by economists and other
social scientists, matching theory implies that hu-
mans may not try to maximize utility (or reinforce-
ment). People (and animals) do not search for the
strategy that yields the greatest overall returns;
they equalize their behavior to the obtained rates
of reinforcement from alternatives. Research sug-
gests that matching (rather than maximizing) oc-
curs because humans focus on the immediate
effectiveness of their behavior. A person may re-
ceive a per-hour average of $10 and $5 respectively
from the left and right handles of a slot machine.
Although the left side generally pays twice as
much, there are local periods when the left option
actually pays less than the right. People respond to
these changes in local rate of reinforcement by switch-
ing to the lean alternative (i.e., the right handle),
even though they lose money overall. The general
implication is that human impulsiveness ensures
that choice is not a rational process of getting the
most in the long run but a behavioral process of
doing the best at the moment (Herrnstein 1990).
MATHEMATICS AND BEHAVIOR
MODIFICATIONThe matching law suggests that operant behavior
is determined by the rate of reinforcement for one
alternative relative to all other sources of rein-
forcement. Even in situations that involve a single
response on a schedule of reinforcement, the
behavior of organisms is regulated by alternative
sources of reinforcement. A rat that is pressing a
lever for food may gain additional reinforcement
from exploring the operant chamber, scratching
itself, and so on. In a similar fashion, rather than
work for teacher attention a pupil may look out
the window, talk to a friend, or even daydream.
Thus in a single-operant setting, multiple sources
of reinforcement are functioning. Herrnstein (1970)
argued this point and suggested an equation for
the single operant that is now called the quantita-
tive law of effect.Carr and McDowell (1980) applied Herrnstein’s
equation to a clinically relevant problem. The case
involved the treatment of a 10-year-old boy who
repeatedly and severely scratched himself. Before
treatment the boy had a large number of open
sores on his scalp, face, back, arms, and legs. In
addition, the boy’s body was covered with scabs,
scars, and skin discoloration. In their review of this
case, Carr and McDowell demonstrated that the
boy’s scratching was operant behavior. Careful
observation showed that the scratching occurred
more often when he and other family members
were in the living room watching television. This
suggested that a specific situation set the occasion
for the self-injurious behavior. Further observa-
tion showed that family members repeatedly and
reliably reprimanded the boy when he engaged in
self-injury. Reprimands are seemingly negative
events, but adult attention (whether negative or
positive) can serve as reinforcement for children’s
behavior.In fact, McDowell (1981) showed that the boy’s
scratching was in accord with Herrnstein’s equa-
tion (i.e., the quantitative law of effect). He plotted
the reprimands per hour on the x-axis and scatches
per hour on the y-axis. When applied to this data,
the equation provided an excellent description of
the boy’s behavior. The quantitative law of effect
also suggested how to modify the problem behav-
ior. In order to reduce scratching (or any other
problem behavior), one strategy is to increase
reinforcement for alternative behavior. As rein-
forcement is added for alternative behavior, prob-
lem behavior must decrease; this is because the
reinforcement for problem behavior is decreasing
(relative to total reinforcement) as reinforcement
is added to other (acceptable) behavior.