Matching law

Quantitative relationship
In operant conditioning, the matching law is a quantitative relationship that holds between the relative rates of response and the relative rates of reinforcement in concurrent schedules of reinforcement. For example, if two response alternatives A and B are offered to an organism, the ratio of response rates to A and B equals the ratio of reinforcements yielded by each response. This law applies fairly well when non human subjects are exposed to concurrent variable interval schedules (but see below); its applicability in other situations is less clear, depending on the assumptions made and the details of the experimental situation. The generality of applicability of the matching law is subject of current debate. The matching law can be applied to situations involving a single response maintained by a single schedule of reinforcement if one assumes that alternative responses are always available to an organism, maintained by uncontrolled "extraneous" reinforcers. For example, an animal pressing a lever for food might pause for a drink of water. The matching law was first formulated by R. J. Herrnstein (1961) following an experiment with pigeons on concurrent variable interval schedules. Pigeons were presented with two buttons in a Skinner box, each of which led to varying rates of food reward. The pigeons tended to peck the button that yielded the greater food reward more often than the other button, and the ratio of their rates to the two buttons matched the ratio of their rates of reward on the two buttons.

There are three ideas on how humans and animals maximize reinforcement, molecular maximizing, molar maximizing and melioration. molecular maximizing: organisms always choose whichever response alternative is most likely to be reinforced at the time. molar maximizing: organisms distribute their responses among various alternatives so as to maximize the amount of reinforcement they earn over the long run. melioration: literally means to "make better"; organisms respond so as to improve the local rates of reinforcement for response alternatives. behavior keeps shifting towards the better of two alternatives until ratios are equal which makes matching.

The matching law is theoretically important for several reasons. First, it offers a simple quantification of behavior that can be applied to a number of situations. Secondly, offers a lawful account of choice. As Herrnstein (1970) expressed it, under an operant analysis, choice is nothing but behavior set into the context of other behavior. The matching law thus challenges the idea that choice is an unpredictable outcome of free will, just as B. F. Skinner and others have argued. However this challenge becomes serious only if it applies to human behavior, as well as to the behavior of pigeons and other animals. When human participants perform under concurrent schedules of reinforcement, matching has been observed in some experiments, but wide deviations from matching have been found in others. Finally, if nothing else, the matching law is important because it has generated a great deal of research that has widened our understanding of operant control.

The matching law, and the generalized matching law, have helped behavior analysts to understand some complex human behaviors, especially the behavior of children in certain conflict situations. James Snyder and colleague have found that response matching predicts the use of conflict tactics by children and parents during conflict bouts. This matching rate predicts future arrests. Even children's use of deviant talk appears to follow a matching pattern.