Modelling collective opinion formation by means of active Brownian particles


The concept of active Brownian particles is used to model a collective opinion formation process. It is assumed that individuals in community create a two-component communication field that influences the change of opinions of other persons and/or can induce their migration. The communication field is described by a reaction-diffusion equation, the opinion change of the individuals is given by a master equation, while the migration is described by a set of Langevin equations, coupled by the communication field. In the mean-field limit holding for fast communication we derive a critical population size, above which the community separates into a majority and a minority with opposite opinions. The existence of external support (e.g. from mass media) changes the ratio between minority and majority, until above a critical external support the supported subpopulation exists always as a majority. Spatial effects lead to two critical “social” temperatures, between which the community exists in a metastable state, thus fluctuations below a certain critical wave number may result in a spatial opinion separation. The range of metastability is particularly determined by a parameter characterizing the individual response to the communication field. In our discussion, we draw analogies to phase transitions in physical systems.

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Received 26 November 1999

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Schweitzer, F., Hołyst, J. Modelling collective opinion formation by means of active Brownian particles. Eur. Phys. J. B 15, 723–732 (2000).

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  • PACS. 05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion - 05.65.+b Self-organized systems - 87.23.Ge Dynamics of social systems