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A problem with using derivatives to explain the matching law
1Economics Dept., 164 FOB, Brigham Young University, Provo, Utah 84602, USA.
Behavioural Processes
|June 14, 2014
Summary
Herrnstein's proposed differential equation for the matching law was found to be unstable. This mathematical model cannot explain the consistent matching behavior observed in studies.
Area of Science:
- Behavioral psychology
- Mathematical modeling
- Dynamical systems theory
Background:
- The matching law is a fundamental principle in behavioral psychology, describing how organisms allocate responses between concurrent schedules of reinforcement.
- Herrnstein (1979) proposed a novel derivation of the matching law from an ordinary differential equation, aiming to provide a dynamic basis for the law.
Purpose of the Study:
- To analyze the dynamic properties of Herrnstein's (1979) proposed ordinary differential equation for the matching law.
- To determine if Herrnstein's equation can account for the widely observed phenomenon of matching behavior.
Main Methods:
- Analysis of the stability properties of the ordinary differential equation proposed by Herrnstein (1979).
- Examination of the long-term behavioral predictions derived from the equation's dynamics.
Main Results:
- Herrnstein's (1979) differential equation exhibits inherent dynamic instability.
- The proposed equation predicts that behavior cannot stabilize in accordance with the matching law, contradicting empirical observations.
Conclusions:
- Herrnstein's (1979) differential equation is inadequate for explaining the matching law.
- The dynamic properties of the equation preclude it from accounting for the consistent matching behavior observed in numerous studies.
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