Neighborhood models of minority opinion spreading

Maxi San Miguel

Instituto Mediterraneo de Estudios Avanzados, IMEDEA (CSIC-UIB), Ed. Mateu Orfila, Campus Universitat Illes Balears, E-07122 Palma de Mallorca, Spain

We reconsider a model of minority opinion spreading introduced by S. Galam to discuss basic mechanisms of social inertia resulting in democratic rejection of social reforms initially favored by a majority. In this model there exists a threshold value p_c < \x{00BD} for the initial concentration p of individuals against the social reform such that for p > p_c every individual eventually adopts the opinion of the initial minority, so that the social reform is rejected and the social status quo is maintained. We incorporate local interactions in the model, as appropriate, for example, for a primitive society in which individuals interact very predominantly with their neighbors. However, the size of the neighborhood (meeting cell) in which the interaction takes place changes in every cycle of the dynamics. We find that p_c goes to zero as the number of individuals goes to infinity: The threshold value for the initial concentration of individuals against the social reform vanishes with growing size of the population, so that the social reform is always rejected. This happens because a critical size for an initial local domain of minority supporters exists. Domains of larger size will grow and occupy the whole system. A domain of overcritical size always exists in the limit of infinitely large systems.