Probability Distribution Dynamics Explaining Agent Model Convergence to Extremism

Abstract

This chapter studies continuous opinion models with extremists, and we use probability distribution models which approximate the behaviour of agents based models in order to explain their attractor patterns. The probability distribution is defined on a discrete grid in the opinion / uncertainty space. We compute the equations of probability flows between each couple of sites of the grid for different variants of the opinion influence model (bounded confidence, relative agreement and two others). The simulations show that the probability distribution models yield attractor patterns very similar to those obtained with the agent based models. Moreover, a study of the probability distribution evolution helps to better understand the process of convergence to single and double extreme attractors observed in agent based models.