Opinion dynamics model with weighted influence: Exit probability and dynamics

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.