The Generality of Matching
This equality of the rates of both response and reinforcement is called a law of behavior, because it describes how a variety of organisms choose among alternatives (de Villiers, 1977). Animals such as pigeons (Davison & Ferguson, 1978), wagtails (Houston, 1986), cows (Matthews & Temple, 1979), and rats (Poling, 1978) have demonstrated matching in choice situations. Interestingly, this same law applies to humans in a number of different settings (Bradshaw & Szabadi, 1988; Pierce & Epling, 1983). Reinforcers have ranged from food (Herrnstein, 1961b) to points that are subsequently exchanged for money (Bradshaw, Ruddle, & Szabadi, 1981). Behavior has been as diverse as lever pressing by rats (Norman & McSweeney, 1978) and conversation in humans (Conger & Killeen, 1974; Pierce, Epling, & Greer, 1981). Environments in which matching has been observed have included T-mazes, operant chambers, and open spaces with free-ranging flocks of birds (Baum, 1974a) as well as discrete-trial and free operant choice by human groups (Madden, Peden, & Yamaguchi, 2002). Also, special education students have been found to spend time on math problems
proportional to the relative rate of reinforcement (e.g., Mace, Neef, Shade, & Mauro, 1994). Thus, the matching law describes the distribution of individual (and group) behavior across species, type of response, reinforcers, and settings.
An interesting test of the matching law was reported by Conger and Killeen (1974). These researchers assessed human performance in a group-discussion situation. A group was composed of three experimenters and one subject. The subject was not aware that the other group members were confederates in the experiment and was asked to discuss attitudes toward drug abuse. One of the confederates prompted the subject to talk. The other two confederates were assigned the role of an audience. Each listener reinforced the subject's talk with brief positive words or phrases when a hidden cue light came on. The cue lights were scheduled so that the listeners gave different rates of reinforcement to the speaker. When the results for several subjects were combined, the relative time spent talking to the listener matched relative rate of agreement from the listener. These results suggest that the matching law operates in everyday social interaction.
Of course, in the complex world of people and other animals, matching does not always occur (Baum, 1974b). This is because in complex environments, contingencies of positive and negative reinforcement may interact, reinforcers differ in value, and histories of reinforcement are not controlled. In addition, discrimination of alternative sources of reinforcement may be weak or absent. For example, pretend you are talking to two people after class at the local bar and grill. You have a crush on one of these two, and the other you do not really care for. Both of these people attend to your conversation with equal rates of social approval, eye contact, and commentary. You can see that even though the rates of reinforcement are the same, you will probably spend more time talking to the person you like best. Because this is a common occurrence in the nonlaboratory world, you might ask, "What is the use of matching, and how can it be a law of behavior?"
The principle of matching is called a law, because it describes the regularity underlying choice. Many scientific laws work in a similar fashion. Anyone who has an elementary understanding of physics can tell you that objects of equal mass fall to the earth at the same rate. Observation, however, tells you that a pound of feathers and a pound of rocks do not fall at the same velocity. We can only see the lawful relations between mass and rate of descent when other conditions are controlled. In a vacuum, a pound of feathers and a pound of rocks fall at equal rates, and the law of gravity is observed. Similarly, with appropriate laboratory control, the relative rate of response matches the relative rate of reinforcement.
Behavioral choice can also be measured as time spent on an alternative (Baum & Rachlin, 1969; Brownstein & Pliskoff, 1968). Time spent is a useful measure of behavior when the response is continuous, as in talking to another person. In the laboratory, rather than measure the number of responses, the time spent on an alternative may be used to describe the distribution of behavior. The matching law can also be expressed in terms of the relative time spent on an alternative. Equation 9.2 is similar to Equation 9.1 but states the matching relationship in terms of time:
In this equation, the time spent on alternative A is represented by Ta, and the time spent on alternative B is Tb. Again, Ra and Rb represent the respective rates of reinforcement for these alternatives. The equation states that relative time spent on an alternative equals the relative rate of reinforcement from that alternative. This extension of the matching law to continuous responses such as standing in one place or looking at objects is important. Most behavior outside of the laboratory does not occur as discrete responses. In this case, Equation 9.2 may be used to describe choice and preference.
Equations 9.1 and 9.2 state that relative behavior matches the relative rate of reinforcement. A consideration of either equation makes it evident that to change behavior, the rate of reinforcement for the target response may be changed; alternatively, the rate of reinforcement for other concurrent operants may be altered. Both of these procedures change the relative rate of reinforcement for the specified behavior. Equation 9.3 represents the relative rate of response as a function of several alternative sources of reinforcement:
Ba/(Ba + Bb + ... Bn) = Ra/(Ra + Rb + . . . Rn). (9.3)
In the laboratory, most experiments are conducted with only two concurrent schedules of reinforcement. However, the matching law also describes the situation in which an organism may choose among several sources of reinforcement (Davison & Hunter, 1976; Elsmore & McBride, 1994; Miller & Loveland, 1974; Pliskoff & Brown, 1976). In Equation 9.3, behavior allocated to alternative A (Ba) is expressed relative to the sum of all behavior directed to the known alternatives (Ba + Bb + ... Bn). Reinforcement provided by alternative A (Ra) is stated relative to all known sources of reinforcement (Ra + Rb + ... Rn). Again, notice that an equality of proportions (matching) is stated.
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