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Related Experiment Videos

On Herrnstein's equation and related forms.

J E Staddon

    Journal of the Experimental Analysis of Behavior
    |September 1, 1977
    PubMed
    Summary

    Herrnstein's equation, describing response and reinforcement rates, has a strong empirical basis but an uncertain theoretical foundation. This study explores two derivations, offering insights into its utility in interval schedules.

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    Area of Science:

    • Behavioral psychology
    • Mathematical psychology

    Background:

    • Herrnstein's 1970 equation models the relationship between response rates and reinforcement rates in interval schedules.
    • While empirically supported, the theoretical underpinnings of this equation remain debated.

    Purpose of the Study:

    • To explore two distinct theoretical approaches for deriving Herrnstein's equation.
    • To investigate potential modifications and alternative formulations of the equation.

    Main Methods:

    • Derivation of the equation as an equilibrium solution to linear-operator learning models.
    • Exploration of power-function formulations as modifications.
    • Derivation from an assumption of response strength proportional to reinforcement rate with a response ceiling.

    Main Results:

    • The equation can be derived from learning models and from a threshold assumption (momentary maximizing).
    • A threshold assumption implies correlated parameters in Herrnstein's equation.
    • This correlation may explain the equation's effectiveness with interval schedules.

    Conclusions:

    • Two distinct theoretical pathways can lead to Herrnstein's equation.
    • The derivation from a threshold assumption provides a potential explanation for the equation's empirical success in interval schedules.
    • Further research into these derivations can refine our understanding of response-reinforcement relationships.

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