On the emergence of an ‘intention field’ for socially cohesive agents.

Summary 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 Borghesi and Bouchaud (2010 Eur. Phys. J. B?75 395) and Borghesi et?al (2012 PLoS One?7 e36289). 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.