  We introduce a stochastic model of binary opinion dynamics in which the
opinions are determined by the size of the neighbouring domains. The exit
probability here shows a step function behaviour indicating the existence of a
separatrix distinguishing two different regions of basin of attraction. This
behaviour, in one dimension, is in contrast to other well known opinion
dynamics models where no such behaviour has been observed so far. The
coarsening study of the model also yields novel exponent values. A lower value
of persistence exponent is obtained in the present model, which involves
stochastic dynamics, when compared to that in a similar type of model with
deterministic dynamics. This apparently counter-intuitive result is justified
using further analysis. Based on these results it is concluded that the
proposed model belongs to a unique dynamical class.
