Pairwise stochastic bounded confidence opinion dynamics: Heavy tails and stability

Traditional models in opinion dynamics involve agents updating their opinions based on the opinions of their neighbors in a static social-graph, regardless of their differences in opinions. In contrast, the bounded confidence opinion dynamics does not presume a static interaction graph, and instead models interactions between those agents that share similar opinions (i.e., are close to one another, capturing online discussion groups and conventional meetings). We generalize the bounded confidence opinion dynamics model by incorporating pairwise stochastic interactions based on opinion differences as well as the self or endogenous evolution of the agent opinions, which is represented by a random process. We analytically characterize the conditions under which this stochastic dynamics is stable in an appropriate sense. This characterization relates well to what is observed in social systems. Moreover, this generalization sheds light on dynamics that combine aspects of graph-based updates and bounded confidence models.