Novel Multidimensional Models of Opinion Dynamics in Social Networks

TL;DR

This paper introduces a new multidimensional opinion dynamics model for social networks that accounts for interdependent topics and analyzes its stability and convergence properties, including asynchronous protocols.

Contribution

It presents a novel multidimensional extension of opinion models that captures topic interdependence and examines stability and convergence, including asynchronous communication.

Findings

Model captures interdependent opinions on multiple topics.

Proves stability and convergence of the model.

Shows asynchronous protocols reach similar final opinions.

Abstract

Unlike many complex networks studied in the literature, social networks rarely exhibit unanimous behavior, or consensus. This requires a development of mathematical models that are sufficiently simple to be examined and capture, at the same time, the complex behavior of real social groups, where opinions and actions related to them may form clusters of different size. One such model, proposed by Friedkin and Johnsen, extends the idea of conventional consensus algorithm (also referred to as the iterative opinion pooling) to take into account the actors' prejudices, caused by some exogenous factors and leading to disagreement in the final opinions. In this paper, we offer a novel multidimensional extension, describing the evolution of the agents' opinions on several topics. Unlike the existing models, these topics are interdependent, and hence the opinions being formed on these topics are also mutually dependent. We rigorous examine stability properties of the proposed model, in particular, convergence of the agents' opinions. Although our model assumes synchronous communication among the agents, we show that the same final opinions may be reached "on average" via asynchronous gossip-based protocols.