  We investigate the long-time dynamics of an opinion formation model inspired
by a work by Borghesi, Bouchaud and Jensen. Firstly, we derive a Fokker-Planck
type equation under the assumption that interactions between individuals
produce little consensus of opinion (grazing collision approximation).
Secondly, we study conditions under which the Fokker-Planck equation has
non-trivial equilibria and derive the macroscopic limit (corresponding to the
long-time dynamics and spatially localized interactions) for the evolution of
the mean opinion. Finally, we compare two different types of interaction rates:
the original one given in the work of Borghesi, Bouchaud and Jensen (symmetric
binary interactions) and one inspired from works by Motsch and Tadmor
(non-symmetric binary interactions). We show that the first case leads to a
conservative model for the density of the mean opinion whereas the second case
leads to a non-conservative equation. We also show that the speed at which
consensus is reached asymptotically for these two rates has fairly different
density dependence.
