Opinion Formation and Phase Transitions in a Probabilistic Cellular Automaton with Two Absorbing States - Cellular Automata - page 249

Opinion Formation and Phase Transitions in a
Probabilistic Cellular Automaton with Two
Absorbing States

Franco Bagnoli 1 , 4 , Fabio Franci 2 , 4 , and Raul Rechtman 3

1

(Dipartimento di Energetica, Universita di Firenze,
Via S. Marta, 3 I-50139 Firenze, Italy. [e-mail]
2

Dipartimento di Sistemi e Informatica, Universita di Firenze,
Via S. Marta, 3 I-50139 Firenze, Italy. [e-mail]
3

Centro de Investigac ıon en Energ ıa, UNAM,
62580 Temixco, Morelos, Mexico. [e-mail]
4

INFM, Sezione di Firenze.

Abstract. We discuss the process of opinion formation in a completely
homogeneous, democratic population using a class of probabilistic cellu-
lar automata models with two absorbing states. Each individual can have
one of two opinions that can change according to that of his neighbors.
It is dominated by an overwhelming majority and can disagree against
a marginal one. We present the phase diagram in the mean field ap-
proximation and from numerical experiments for the simplest nontrivial
case. For arbitrarily large neighborhoods we discuss the mean field re-
sults for a non-conformist society, where each individual adheres to the
overwhelming majority of its neighbors and choses an opposite opinion in
other cases. Mean field results and preliminary lattice simulations with
long-range connections among individuals show the presence of coherent
temporal oscillations of the population.

1 Modeling Social Pressure and Political Transitions

What happens to a society when a large fraction of people switches from a con-
formist to a non-conformist attitude? Is the transition smooth or revolutionary?
These important questions, whose answers can make the difference between two
well-known political points of view, is approached using a theoretical model, in
the spirit of Latane's social impact theory [1,2].
We assume that one's own inclination towards political choices originates
from a mixture of a certain degree of conformism and non-conformism. Con-
formists tend to agree with the local community majority, that is with the av-
erage opinion in a given neighborhood, while non-conformists do the opposite.
However, an overwhelming majority in the neighborhood (which includes the
subject itself) is always followed.
We shall study here the case of a homogeneous population, i.e. a homoge-
neous democratic society. 1 It may be considered as the annealed version of a
1

The case with strong leader was studied in Ref [3].