Handbook of Psychology, Volume 4: Experimental Psychology

Instrumental Responding 381

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% RESPONSES ON KEY A

% REINFORCEMENTS ON KEY A

055

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641

Figure 13.2 The proportion of responses made to one of two keys as a

function of the reinforcers obtained on that key, for three pigeons responding

on concurrent VI, VI schedules. The diagonal line indicates perfect matching

(Equation 13.1). Source:From Herrnstein (1961). Copyright 1961 by the

Society for the Experimental Analysis of Behavior, Inc.

broadly applicable to a range of situations. Interestingly, this
pursuit has been inspired by research on choice—situations in
which more than one reinforced instrumental response is
available at the same time.
Four experimental procedures have figured prominently
in research on the quantitative determiners of instrumental
responding. In thesingle-schedule procedure,the subject
may make a specific response that produces a reinforcer ac-
cording to a given schedule. Inconcurrent schedules,two or
more schedules are available simultaneously and the subject is
free to allocate its behavior across the alternatives. Inmultiple
schedules,access to different reinforcement schedules occurs
successively, with each schedule signaled by a distinctive
(discriminative) stimulus. Finally, in theconcurrent-chains
procedure(and a discrete-trial variant, theadjusting-delay
procedure), subjects choose between two discriminative stim-
uli that are correlated with different reinforcement schedules.
A seminal study by Herrnstein (1961) was the first para-
metric investigation of concurrent schedules. He arranged
two VI schedules in a Skinner box for pigeons, each schedule
associated with a separate manipulandum (i.e., plastic peck-
ing key). Reinforcement was a brief period (3 s) of access to
grain. Pigeons were given extensive training (often 30 or
more sessions) with a given pair of schedules (e.g., VI 1-min,
VI 3-min schedules) until response allocation was stable. The
schedules were then changed across a number of experimen-
tal conditions, such that the relative rate of reinforcement
provided by responding to the left and right keys was varied
while keeping constant the overall programmed reinforce-
ment rate (40/hr). Herrnstein found that the relative rate of re-
sponding to each key was approximately equal to the relative
rate of reinforcement associated with each key. His data,
shown in Figure 13.2, demonstrate what has come to be
known as the matching law:

 or alternatively stated 

(13.1)
In Equation 13.1, BLandBRare the number of responses
made to the left and right keys, and RLandRRare the rein-
forcements earned by responding at those keys. Although
Equation 13.1 might appear tautological, it is important to
note that the matching relation was not forced in Herrnstein’s
study, because responses substantially outnumbered rein-
forcers. Subsequent empirical support for the matching law
has been obtained with a variety of different species, re-
sponses, and reinforcers, and thus it may represent a general
principle of choice (for reviews, see Davison & McCarthy,
1988; B. A. Williams, 1988, 1994a). The matching law seems

RL



RLRR

BL



BLBR

RL



RR

BL



BR

to embody a relativistic law of effect: The relative strength

of an instrumental response depends on the relative rate of

reinforcement maintaining it, which parallels the relativism

evident in most expression-focused models of Pavlovian

conditioning (see this chapter’s section entitled, “Expression-

Focused Models”) and probability matching in the decision-

making literature.

Why Does Matching Occur?

Many investigators have accepted the matching relation as an

empirical rule for choice under concurrent VI-VI schedules.

An important goal, then, is to discover exactly why matching

should occur. Because an answer to this question might pro-

vide insight into the fundamental behavioral processes deter-

mining choice, testing different theories of matching has

been a vigorous topic of research over the past 35 years.

Shimp (1966, 1969) showed that if subjects always re-

sponded to the alternative with the immediate higher proba-

bility of reinforcement, then matching would be obtained.

According to his theory, called momentary maximizing,

responses should show a definite sequential dependence. The

reason is that both schedules run concurrently, so eventually

a response to the leaner alternative is more likely to be rein-

forced. For example, with concurrent Left Key VI 1-min,