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Statistical models based on probability laws, and originally used for the description of the dynamic development of an ensemble of interacting spins, are reformulated in order to study the structure of social groups of individuals mutually influencing each other with respect to their decision behaviour. After a description of the general features of these models, and relating them to the polarization phenomena in society, a quantitative model is developed which can be compared with the decision behaviour of social groups.

A general concept is presented which allows of setting up mathematical models for stochastic and quasi deterministic dynamic processes in social systems.The basis of this concept is the master equation for the probability distribution over appropriately chosen personal and material macrovariables of the society. The probabilistic transition rates depend on motivation potentials governing the decisions and actions of the social agents. The transition from the probability distribution to quasi-meanvalues leads to in general nonlinear coupled differential equations for the macrovariables of the chosen social sector. Up to now several models about population dynamics, collective political opinion formation, dynamics of economic processes and the formation of settlements have been published.