ABSTRACT
The matching law suggests that operant behavior is determined by the rate of reinforcement for one alternative relative to all other known sources of reinforcement. Even in situations in which a contingency exists between a single response and a reinforcement schedule, organisms may have several reinforced alternatives that are unknown to the researcher. Also, many of the activities that produce reinforcement are beyond experimental control. A rat that is lever pressing 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, even in a single-operant setting, multiple sources of reinforcement are operating. Richard Herrnstein (1970, 1974) argued this point and suggested that all operant behavior must be understood as behavior emitted in the context of other alternative sources of reinforcement. Based on these ideas, Herrnstein proposed a matching equation that describes the absolute rate of response on a single schedule of reinforcement. This mathematical formulation is called the quantitative law of effect. The law states that the absolute rate of response on a schedule of reinforcement is a hyperbolic function of rate of reinforcement on the schedule relative to the total rate of reinforcement, both scheduled and extraneous reinforcement. That is, as the rate of reinforcement on the schedule increases, the rate of response also rises, but eventually further increases in the rate of reinforcement produce less and less of an increase in the rate of response (hyperbolic). Also, the rise in the rate of response with an increasing rate of reinforcement is modified by extraneous sources of reinforcement. The greater the extraneous reinforcement the less the increase in rate of response with increasing rate of scheduled reinforcement. One implication is that control of behavior by a schedule of reinforcement is reduced as the sources of extraneous reinforcement increase.
