We describe here a possible approach to the formation of choice in a society bymethods borrowed from the kinetic theory of rarefied gases. It is shown thatthe evolution of the continuous density of opinions obeys a linear Boltzmannequation where the background density represents the fixed distribution ofpossible choices. The binary interactions between individuals are in generalnon-local, and take into account both the compromise propensity and theself-thinking. In particular regimes, the linear Boltzmann equation is welldescribed by a Fokker-Planck type equation, for which in some cases the steadystates (distribution of choices) can be obtained in analytical form. ThisFokker-Planck type equation generalizes analogous one obtained by mean fieldapproximation of the voter model in [27]. Numerical examples illustratethe influence of different model parameters in the description both of theshape of the distribution of choices, and in its mean value.
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Comincioli et al. (2009) studied this question.
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