A Mathematical Foundation for Stochastic Opinion Dynamics

This article presents a stochastic opinion dynamics model where (a) the opinion of each agent in a network is modeled as a probability distribution as against a point object, (b) consensus is defined as the stability region of the ensuing set of stochastic difference equations, and (c) compromise solutions can be derived between agents who don't have a consensus. The model is well suited for tracking opinion dynamics over large online systems such as Twitter and Yelp where opinions need to be extracted from the user-generated text data. Theoretical conditions for the existence of consensus and the impact that stubborn agents have on opinion dynamics are also presented.