On the exponent in the "generalized" matching equation.
A power function equation between ratios of behavior and ratios of reinforcement rates has been called a generalized form of Herrnstein's (1961) matching law, even without a formal relationship having been shown between the two equations. The present work uses a functional relationship to prove that when ratios of reinforcement are not equivalent to ratios of behavior, and the transform leading to this inequality is consistent for every pair of reinforcement rates, the result is a power function relationship between response and reinforcement ratios. The label "generalized matching equation" for the power function equation is thus validated formally.
Allen
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CM