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A suggestion for a new approach to the mathematical theory of imitative behavior

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Abstract

The theory of imitative behavior as developed hitherto by the author was based on the assumption that each individual has a natural preference for one of the two mutually exclusive behaviors. The endogenous fluctuations in the central nervous system then result in the individual’s exhibiting the two behaviors alternately with a relative frequency determined by the natural preference. Imitation shifts the natural preference towards one or the other of the two mutually exclusive behaviors. In the present approach it is suggested that the relative frequency of the two mutually exclusive behaviors exhibited alternately is determined by maximizing the “satisfaction function” of the individual, that is by hedonistic factors rather than by purely random fluctuations. Corresponding equations are developed. It is shown that in certain cases, even when the imitation effect is absent, a sort of “pseudoimitation” may occur. Another situation leads, in the case of two individuals only, to a complete “division of labor” between them, with respect to the two behaviors. Each one exhibits only one behavior. After that imitation is introduced explicitly by assuming that imitation by one individual or another increases the satisfaction function of the imitating individual. Results thus obtained show similarities to the results of the old theory.

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Authors and Affiliations

  1. Mental Health Research Institute, University of Michigan, Ann Arbor, Michigan

    N. Rashevsky

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  1. N. Rashevsky
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Rashevsky, N. A suggestion for a new approach to the mathematical theory of imitative behavior. Bulletin of Mathematical Biophysics 29, 863–877 (1967). https://doi.org/10.1007/BF02476933

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  • DOI: https://doi.org/10.1007/BF02476933

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