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A Mathematical Model of Group Social Interaction

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  • R G V Baker

    (Department of Geography, University of New South Wales, Sydney, Australia)

Abstract

The definition of place utility from potential theory shows that a preference and orthogonal indifference field can influence a decisionmaker, which suggests the operation of behavioural forces. Learning energy is defined to be a major behavioural force and a statistical model is proposed for its distribution over an assembly of decisionmakers. An attitude system is derived for a social network where the decisionmaker can be in a unitary state of utility or disutility. The resulting partition function shows that the learning energy of the assembly is derived from nearest-neighbour interactions and the operation of an external place utility preference field. A positive linear relationship is proposed between learning energy and environmental stress. The critical stress in social interaction is determined and a variety of behaviours in urban sociology are predicted. The model is then applied to a Markov learning system and the results discussed.

Suggested Citation

  • R G V Baker, 1982. "A Mathematical Model of Group Social Interaction," Environment and Planning A, , vol. 14(8), pages 1031-1046, August.
    • Handle: RePEc:sae:envira:v:14:y:1982:i:8:p:1031-1046
    DOI: 10.1068/a141031
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