Information about Matching Law
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. It applies reliably when non-human subjects are exposed to concurrent variable interval schedules; its applicability in other situations is less clear, depending on the assumptions made and the details of the experimental situation.
Stated simply, the matching law suggests that an animal's response rate to a scenario will be proportionate to the amount/duration of postive reinforcement delivered.
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 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; however, they did so at a rate that was similar to the rate of reward.
If R1 and R2 are the rate of responses on two schedules that yield obtained (as distinct from programmed) rates of reinforcement Rf1 and Rf2, the strict matching law holds that the relative response rate R1/(R1+R2) matches, that is, equals, the relative reinforcement rate Rf1/(Rf1+Rf2). That is,
This relationship can also be stated in terms of response and reinforcement ratios:
Subsequent research has shown that data normally depart from strict matching, but are fitted to a very good approximation by a power function generalization of the strict matching (Baum, 1974),
This is more conveniently expressed in logarithmic form
The constants b and s are referred to as bias and sensitivity respectively. This generalized matching law accounts for high proportions of the variance in most experiments on concurrent variable interval schedules in non-humans. Values of b depend on details of the experiment set up, but values of s are consistently found to be around 0.8, whereas the value required for strict matching would be 1.0 (Baum, 1974; Davison & McCarthy, 1988).
The matching law is theoretically important for two reasons. First, it offers a simple quantification of behaviour which is capable of extension to a number of other situations. Secondly, it appears to offer a lawful, predictive account of choice; as Herrnstein (1970) expressed it, under an operant analysis, choice is nothing but behavior set into the context of other behavior. It thus challenges any idea of free will, in exactly the way B. F. Skinner had argued that the experimental analysis of behavior should, in his book Beyond freedom and dignity. However this challenge is only serious if the scope of the matching law can be extended from pigeons to humans. When human participants perform under concurrent schedules of reinforcement, matching has been observed in some experiment (e.g. Bradshaw et al, 1976), but wide deviations from matching have been found in others (e.g. Horne & Lowe, 1993). The matching law has generated a great deal of research, much of it presented to the Society for Quantitative Analysis of Behavior.
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Stated simply, the matching law suggests that an animal's response rate to a scenario will be proportionate to the amount/duration of postive reinforcement delivered.
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 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; however, they did so at a rate that was similar to the rate of reward.
If R1 and R2 are the rate of responses on two schedules that yield obtained (as distinct from programmed) rates of reinforcement Rf1 and Rf2, the strict matching law holds that the relative response rate R1/(R1+R2) matches, that is, equals, the relative reinforcement rate Rf1/(Rf1+Rf2). That is,
The matching law is theoretically important for two reasons. First, it offers a simple quantification of behaviour which is capable of extension to a number of other situations. Secondly, it appears to offer a lawful, predictive account of choice; as Herrnstein (1970) expressed it, under an operant analysis, choice is nothing but behavior set into the context of other behavior. It thus challenges any idea of free will, in exactly the way B. F. Skinner had argued that the experimental analysis of behavior should, in his book Beyond freedom and dignity. However this challenge is only serious if the scope of the matching law can be extended from pigeons to humans. When human participants perform under concurrent schedules of reinforcement, matching has been observed in some experiment (e.g. Bradshaw et al, 1976), but wide deviations from matching have been found in others (e.g. Horne & Lowe, 1993). The matching law has generated a great deal of research, much of it presented to the Society for Quantitative Analysis of Behavior.
References
- Baum, W. M. (1974). On two types of deviation from the matching law: Bias and undermatching. Journal of the Experimental Analysis of Behavior, 22, 231-242.
- Bradshaw, C. M., Szabadi, E., & Bevan, P. (1976). Behavior of humans in variable-interval schedules of reinforcement Journal of the Experimental Analysis of Behavior, 26, 135–141.
- Davison, M., & McCarthy, D. (1988). The matching law: A research review. Hillsdale, NJ: Erlbaum.
- Herrnstein, R. J. (1961). Relative and absolute strength of responses as a function of frequency of reinforcement. Journal of the Experimental Analysis of Behaviour, 4, 267-272.
- Herrnstein, R. J. (1970). On the law of effect. Journal of the Experimental Analysis of Behavior, 13, 243-266.
- Horne, P. J., & Lowe, C. F. (1993). Determinants of human performance on concurrent schedules. Journal of the Experimental Analysis of Behavior, 59, 29-60. (doi: 10.1901/jeab.1993.59-29).
Operant conditioning is the use of consequences to modify the occurrence and form of behavior. Operant conditioning is distinguished from Pavlovian conditioning in that operant conditioning deals with the modification of "voluntary behavior" through the use of
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In behaviorism, rate of reinforcement is number of reinforcements per time, usually per minute. Symbol of this rate is usually Rf. Its first major exponent was B. F. Skinner (1939). It is used in the Matching Law.
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In operant conditioning, concurrent schedules of reinforcement are schedules of reinforcement that are simultaneously available to an animal subject or human participant, so that the subject or participant can respond on either schedule.
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reinforcement is an increase in the strength of a response following the presentation of a stimulus contingent on that response. Response strength can be assessed by measures such as the frequency with which the response is made (for example, a pigeon may increase the rate at which
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Richard J. Herrnstein (May 20 1930—September 13 1994) was a prominent researcher in animal learning in the Skinnerian tradition. He was one of the founders of Quantitative Analysis of Behavior.
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Columbidae
Subfamilies
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Pigeons and doves constitute the family Columbidae within the order Columbiformes, which include some 300 species of near passerine birds.
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Subfamilies
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Pigeons and doves constitute the family Columbidae within the order Columbiformes, which include some 300 species of near passerine birds.
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Rate of responding
Rate is a ratio between two measurements with different units. Rate of responding is the number of responses per minute, or some other time unit. It is usually written as R. Its first major exponent was B. F. Skinner (1939). It is used in the Matching Law...... Click the link for more information.
359, 1805–1809. Hofstadter, Douglas. (2007) I Am A Strange Loop. Basic Books. ISBN 978-0465030781 Kane, Robert (1998). The Significance of Free Will. New York: Oxford University Press ISBN 0-19-512656-4 Lawhead, William F. (2005).
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Burrhus Frederic Skinner (March 20, 1904 – August 18, 1990), Ph.D. was a highly influential American psychologist, author, inventor, advocate for social reform [1][2][3][4] and poet.
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The experimental analysis of behavior is the name given to school of psychology founded by B. F. Skinner, and based on his philosophy of radical behaviorism. A central principle was the inductive, data-driven[1]
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Beyond Freedom and Dignity is a book-length essay written by American psychologist B. F. Skinner and first published in 1971. The book argued that entrenched belief in free will and the moral autonomy of the individual (which Skinner referred to as "dignity") hindered the
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The Society was founded in 1978 by Michael Lamport Commons and John Anthony Nevin. The first president was Richard J. Herrnstein. In the beginning it was called the Harvard Symposium on Quantitative Analysis of Behavior (HSQAB).
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