On the 1D q-voter model and the Kirkwood approximation
Andre Timpanaro (Instituto de Física, Universidade de São Paulo, Sao Paulo, Brasil)
In this talk I'll begin by examining the q-voter model in one
dimension, showing some recent results that shed some light on
the controversy surrounding its exit probability. Our results
for large networks indicate that while the exit probability is
not a step function, the result p^q/(p^q + (1-p)^q) found in
the literature is also not accurate, with the exception of the
case q=2 (besides the original voter model), corresponding to
the Sznajd model. As in this case the exit probability can be
deduced by a Kirkwood approximation (whose validity has also
been questioned) we decided to study this approximation in a
wide generalization of the Sznajd model, proposed by Kondrat.
Our simulation results show the validity limits of the
approximation, but also confirm a prediction concerning
a non-trivial exit probability, that helps us to understand
what is happening in the q-voter model, a bit better.