Opinion dynamics: models, extensions and external effects

Recently, social phenomena have received a lot of attention not only from social scientists, but also from physicists, mathematicians and computer scientists, in the emerging interdisciplinary field of complex system science. Opinion dynamics is one of the processes studied, since opinions are the drivers of human behaviour, and play a crucial role in many global challenges that our complex world and societies are facing: global financial crises, global pandemics, growth of cities, urbanisation and migration patterns, and last but not least important, climate change and environmental sustainability and protection. Opinion formation is a complex process affected by the interplay of different elements, including the individual predisposition, the influence of positive and negative peer interaction (social networks playing a crucial role in this respect), the information each individual is exposed to, and many others. Several models inspired from those in use in physics have been developed to encompass many of these elements, and to allow for the identification of the mechanisms involved in the opinion formation process and the understanding of their role, with the practical aim of simulating opinion formation and spreading under various conditions. These modelling schemes range from binary simple models such as the voter model, to multi-dimensional continuous approaches. Here, we provide a review of recent methods, focusing on models employing both peer interaction and external information, and emphasising the role that less studied mechanisms, such as disagreement, has in driving the opinion dynamics. [...]Comment: 42 pages, 6 figure

Early fragmentation in the adaptive voter model on directed networks

We consider voter dynamics on a directed adaptive network with fixed out-degree distribution. A transition between an active phase and a fragmented phase is observed. This transition is similar to the undirected case if the networks are sufficiently dense and have a narrow out-degree distribution. However, if a significant number of nodes with low out degree is present, then fragmentation can occur even far below the estimated critical point due to the formation of self-stabilizing structures that nucleate fragmentation. This process may be relevant for fragmentation in current political opinion formation processes.Comment: 9 pages, 8 figures as published in Phys. Rev.

Setting the Agenda: Different strategies of a Mass Media in a model of cultural dissemination

Day by day, people exchange opinions about a given new with relatives, friends, and coworkers. In most cases, they get informed about a given issue by reading newspapers, listening to the radio, or watching TV, i.e., through a Mass Media (MM). However, the importance of a given new can be stimulated by the Media by assigning newspaper's pages or time in TV programs. In this sense, we say that the Media has the power to "set the agenda", i.e., it decides which new is important and which is not. On the other hand, the Media can know people's concerns through, for instance, websites or blogs where they express their opinions, and then it can use this information in order to be more appealing to an increasing number of people. In this work, we study different scenarios in an agent-based model of cultural dissemination, in which a given Mass Media has a specific purpose: To set a particular topic of discussion and impose its point of view to as many social agents as it can. We model this by making the Media has a fixed feature, representing its point of view in the topic of discussion, while it tries to attract new consumers, by taking advantage of feedback mechanisms, represented by adaptive features. We explore different strategies that the Media can adopt in order to increase the affinity with potential consumers and then the probability to be successful in imposing this particular topic.Comment: 23 pages, 7 figure

Moment Closure - A Brief Review

Moment closure methods appear in myriad scientific disciplines in the modelling of complex systems. The goal is to achieve a closed form of a large, usually even infinite, set of coupled differential (or difference) equations. Each equation describes the evolution of one "moment", a suitable coarse-grained quantity computable from the full state space. If the system is too large for analytical and/or numerical methods, then one aims to reduce it by finding a moment closure relation expressing "higher-order moments" in terms of "lower-order moments". In this brief review, we focus on highlighting how moment closure methods occur in different contexts. We also conjecture via a geometric explanation why it has been difficult to rigorously justify many moment closure approximations although they work very well in practice.Comment: short survey paper (max 20 pages) for a broad audience in mathematics, physics, chemistry and quantitative biolog

Coevolutionary dynamics of information spreading and heterophilic link rewiring

In many complex systems, the dynamic processes that take place on a network and the changes in the network topology are intertwined. Here, we propose a model of coevolutionary dynamics of information spreading which is accompanied with link rewiring to facilitate the propagation of information. In our model, nodes possessing information attempt to contact new susceptible nodes through the link rewiring while the information spreads on a network. Using moment-closure and heterogeneous mean-field approximations, we examine both the information spread dynamics and network evolution focusing on epidemic size, epidemic threshold, and degree distributions at the steady state. We found that more frequent heterophilic link rewiring leads to a larger epidemic size but does not alter the epidemic threshold. We also observed that link rewiring results in a broader degree distribution in the steady state. This study provides an insight into the the role of the heterophilic link rewiring in both facilitating information propagation and inducing network heterogeneity.Comment: 6 pages, 4 figure

Modelling opinion dynamics under the impact of influencer and media strategies

Digital communication has made the public discourse considerably more complex, and new actors and strategies have emerged as a result of this seismic shift. Aside from the often-studied interactions among individuals during opinion formation, which have been facilitated on a large scale by social media platforms, the changing role of traditional media and the emerging role of “influencers” are not well understood, and the implications of their engagement strategies arising from the incentive structure of the attention economy even less so. Here we propose a novel framework for opinion dynamics that can accommodate various versions of opinion dynamics as well as account for different roles, namely that of individuals, media and influencers, who change their own opinion positions on different time scales. Numerical simulations of instances of this framework show the importance of their relative influence in creating qualitatively different opinion formation dynamics: with influencers, fragmented but short-lived clusters emerge, which are then counteracted by more stable media positions. The framework allows for mean-field approximations by partial differential equations, which reproduce those dynamics and allow for efficient large-scale simulations when the number of individuals is large. Based on the mean-field approximations, we can study how strategies of influencers to gain more followers can influence the overall opinion distribution. We show that moving towards extreme positions can be a beneficial strategy for influencers to gain followers. Finally, our framework allows us to demonstrate that optimal control strategies allow other influencers or media to counteract such attempts and prevent further fragmentation of the opinion landscape. Our modelling framework contributes to a more flexible modelling approach in opinion dynamics and a better understanding of the different roles and strategies in the increasingly complex information ecosystem