Recent Advances in the Modelling and Analysis of Opinion Dynamics on Influence Networks

A fundamental aspect of society is the exchange and discussion of opinions between individuals, occurring in situations as varied as company boardrooms, elementary school classrooms and online social media. After a very brief introduction to the established results of the most fundamental opinion dynamics models, which seek to mathematically capture observed social phenomena, a brief discussion follows on several recent themes pursued by the authors building on the fundamental ideas. In the first theme, we study the way an individuals self-confidence can develop through contributing to discussions on a sequence of topics, reaching a consensus in each case, where the consensus value to some degree reflects the contribution of that individual to the conclusion. During this process, the individuals in the network and the way they interact can change. The second theme introduces a novel discrete-time model of opinion dynamics to study how discrepancies between an individuals expressed and private opinions can arise due to stubbornness and a pressure to conform to a social norm. It is also shown that a few extremists can create pluralistic ignorance, where people believe there is majority support for a position but in fact the position is privately rejected by the majority. Last, we consider a group of individuals discussing a collection of logically related topics. In particular, we identify that for topics whose logical interdependencies take on a cascade structure, disagreement in opinions can occur if individuals have competing and/or heterogeneous views on how the topics are related, i.e., the logical interdependence structure varies between individuals.