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On the exponent in the "generalized" matching equation.
Journal of the Experimental Analysis of Behavior
|January 1, 1981
Summary
This study formally proves the power function equation is a generalized matching equation. It demonstrates how unequal reinforcement and behavior ratios lead to this power function relationship, validating its label.
Area of Science:
- Behavioral psychology
- Mathematical psychology
Background:
- The power function equation is often considered a generalized form of Herrnstein's matching law.
- A formal mathematical link between the power function and the matching law has been lacking.
Purpose of the Study:
- To formally prove the functional relationship between the power function equation and Herrnstein's matching law.
- To validate the use of the term "generalized matching equation" for the power function.
Main Methods:
- Utilized a functional relationship to analyze the connection between response ratios and reinforcement ratios.
- Investigated scenarios where reinforcement ratios are not equivalent to behavior ratios.
Main Results:
- Demonstrated that a consistent transform leading to unequal reinforcement and behavior ratios results in a power function relationship.
- Formally validated the power function equation as a generalized matching equation.
Conclusions:
- The power function equation is mathematically proven to be a generalized form of the matching law.
- This provides formal validation for the "generalized matching equation" terminology.