Cite as:

Baker R G V, 1982, "A mathematical model of group social interaction" *Environment and Planning A* **14**(8) 1031 – 1046

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**A mathematical model of group social interaction**

**R G V Baker**

Received 6 August 1980, in revised form 13 July 1981

**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.

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