A biased assimilation model on signed graphs

Abstract

This work introduces antagonistic interactions into the so-called biased assimilation model of opinion dynamics, a nonlinear model expressing the bias of the agents towards their own opinions. In this model, opinions exchanged in a signed network are multiplied by a state dependent term having the bias as exponent. For small values of the bias parameters, while for structurally balanced networks polarization always occurs, we show that for structurally unbalanced networks also a state of indecision (corresponding to the centroid of the opinion hypercube) is a local attractor. When instead the biases are all large, the opinions usually polarize. In particular, for large enough biases if all agents take the same initial stance (i.e., are all on the same side of the indecision state), then the opinions polarize all to the same extreme value for both structurally balanced network and structurally unbalanced network.