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proportions are less extreme than the law predicts. Undermatching can happen if subjects too often switch between the two response options, a tendency that may be strengthened by reinforcers that happen to occur just after a subject switches. A changeover delay may be used to reduce the effectiveness of such post-switch reinforcers; typically, this is a 1.5 second interval after a switch when no reinforcer is presented. Overmatching is the opposite of undermatching, and is less common. Here the subjects response proportions are more extreme than reinforcement proportions. Overmatching may occur if there is a penalty for switching. A final deviation is bias, which occurs when subjects spend more time on one alternative than the matching equation predicts. This may happen if a subject prefers a certain environment, area in a laboratory, or method of responding.
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These failures of the matching law have led to the development of the "generalized matching law", which has parameters that reflect the deviations just described. This law is a power function generalization of the strict matching (Baum, 1974), and it has been found to fit a wide variety of matching
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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
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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
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are consistently found to be around 0.8, whereas the value required for strict matching would be 1.0. The concurrent VI VI choice situation involves strong negative feedbacks: the longer the subject refrains from responding to an alternative, the higher his probability of payoff: switching is
455:
A recent review by McDowell reveals that
Herrnstein's original equation fails to accurately describe concurrent-schedule data under a substantial range of conditions. Three deviations from matching have been observed: undermatching, overmatching, and bias. Undermatching means that the response
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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
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are referred to as "bias" and "sensitivity" respectively. "Bias" reflects any tendency the subject may have to prefer one response over the other. "Sensitivity" reflects the degree to which the reinforcement ratio actually impacts the choice ratio. When this equation is plotted, the result is
923:, Gerald R. Patterson, Lynn Schrepferman, Jessica Oeser, Kassy Johnson, and Dana Soetaert (2003): The Application of Response Allocation Matching to Understanding Risk Mechanisms in Development: The Case of Young Children's Deviant Talk and Play, and Risk for Early-Onset Antisocial Behavior.
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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
70:, 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.
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46:. 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
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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.
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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
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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.
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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.
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Snyder, J.J. & Patterson, G.R. (1995). Individualized differences in social aggression: A test of the reinforcement hypothesis in the natural environment.
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molar maximizing: organisms distribute their responses among various alternatives so as to maximize the amount of reinforcement they earn over the long run.
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behavior set into the context of other behavior. The matching law thus challenges the idea that choice is an unpredictable outcome of
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accounts for high proportions of the variance in most experiments on concurrent variable interval schedules in non-humans. Values of
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There are three ideas on how humans and animals maximize reinforcement, molecular maximizing, molar maximizing and melioration.
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690:{\displaystyle \log \left({\frac {R_{1}}{R_{2}}}\right)=\log \left(b\right)+s\cdot \log \left({\frac {Rf_{1}}{Rf_{2}}}\right)}
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Simon, C., & Baum, W. M. (2017). Allocation of Speech in
Conversation. Journal of Experimental Analysis of Behavior, 107.
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Simon, C., & Baum, W. M. (2017). Allocation of Speech in
Conversation. Journal of Experimental Analysis of Behavior, 107.
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molecular maximizing: organisms always choose whichever response alternative is most likely to be reinforced at the time.
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Poling, A., Edwards, T. L., Weeden, M., & Foster, T. (2011). The matching law. Psychological Record, 61(2), 313-322.
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Bradshaw, C.M.; Szabadi, E. & Bevan, P. (1976). Behavior of humans in variable-interval schedules of reinforcement
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Bradshaw, C.M.; Szabadi, E. & Bevan, P. (1976). Behavior of humans in variable-interval schedules of reinforcement
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Herrnstein, R.J. (1961). Relative and absolute strength of responses as a function of frequency of reinforcement.
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Herrnstein, R.J. (1961). Relative and absolute strength of responses as a function of frequency of reinforcement.
447:. That is, for an individual animal, the rate of response is proportional to rate of reinforcement for any task.
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Strand, P.S. (2001) Momentum, Matching, and
Meaning: Toward a Fuller Exploitation of Operant Principles.
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is a quantitative relationship that holds between the relative rates of response and the relative
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Horne, P.J. & Lowe, C.F. (1993). Determinants of human performance on concurrent schedules.
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Horne, P.J. & Lowe, C.F. (1993). Determinants of human performance on concurrent schedules.
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Baum, W.M. (1974). On two types of deviation from the matching law: Bias and undermatching.
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Baum, W.M. (1974). On two types of deviation from the matching law: Bias and undermatching.
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straight line; sensitivity changes the slope and bias changes the intercept of this line.
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on two schedules that yield obtained (as distinct from programmed) rates of reinforcement
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on concurrent variable interval schedules. Pigeons were presented with two buttons in a
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This relationship can also be stated in terms of response and reinforcement ratios:
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Poling, A., Edwards, T. L., Weeden, M., & Foster, T. (2011). The matching law.
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552:{\displaystyle {\frac {R_{1}}{R_{2}}}=b\left({\frac {Rf_{1}}{Rf_{2}}}\right)^{s}}
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often depend on details of the experiment set up, but values of
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Skinner, B. F. (1971)Beyond
Freedom and Dignity, New Yori:Knopf
345:{\displaystyle {\frac {R_{1}}{R_{2}}}={\frac {Rf_{1}}{Rf_{2}}}}
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Alternatively stated, it states that there exists a constant
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Deviations from matching, and the generalized matching law
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This is more conveniently expressed in logarithmic form
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420:{\displaystyle {\frac {R_{i}}{Rf_{i}}}=C}
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58:The matching law was first formulated by
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18:Matching Law
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946:2011-11-17
758:, just as
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