On the emergence of an "intention field" for socially cohesive agents

Abstract

We argue that when a social convergence mechanism exists and is strong enough, one should expect the emergence of a well defined "field", i.e. a slowly evolving, local quantity around which individual attributes fluctuate in a finite range. This condensation phenomenon is well illustrated by the Deffuant-Weisbuch opinion model for which we provide a natural extension to allow for spatial heterogeneities. We show analytically and numerically that the resulting dynamics of the emergent field is a noisy diffusion equation that has a slow dynamics. This random diffusion equation reproduces the long-ranged, logarithmic decrease of the correlation of spatial voting patterns empirically found in [1, 2]. Interestingly enough, we find that when the social cohesion mechanism becomes too weak, cultural cohesion breaks down completely, in the sense that the distribution of intentions/opinions becomes infinitely broad. No emerging field exists in this case. All these analytical findings are confirmed by numerical simulations of an agent-based model.

10 pages, 3 figures

References in corpus (5)

• Statistical physics of social dynamics
• The Dynamics of Crowd Disasters: An Empirical Study
• Self-Organized Criticality model for Brain Plasticity
• Noisy continuous--opinion dynamics
• Diffusing opinions in bounded confidence processes

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