Macroscopic Noisy Bounded Confidence Models with Distributed Radical Opinions

In this article, we study the nonlinear Fokker-Planck (FP) equation that arises as a mean-field (macroscopic) approximation of bounded confidence opinion dynamics, where opinions are influenced by environmental noises and opinions of radicals (stubborn individuals). The distribution of radical opinions serves as an infinite-dimensional exogenous input to the FP equation, visibly influencing the steady opinion profile. We establish mathematical properties of the FP equation. In particular, we (i) show the well-posedness of the dynamic equation, (ii) provide existence result accompanied by a quantitative global estimate for the corresponding stationary solution, and (iii) establish an explicit lower bound on the noise level that guarantees exponential convergence of the dynamics to stationary state. Combining the results in (ii) and (iii) readily yields the input-output stability of the system for sufficiently large noises. Next, using Fourier analysis, the structure of opinion clusters under the uniform initial distribution is examined. Specifically, two numerical schemes for identification of order-disorder transition and characterization of initial clustering behavior are provided. The results of analysis are validated through several numerical simulations of the continuum-agent model (partial differential equation) and the corresponding discrete-agent model (interacting stochastic differential equations) for a particular distribution of radicals

Contrarian compulsions produce time dependent flocking of active particles

Animals having a trend to align their velocities to an average of their neighbors' may flock as illustrated by the Vicsek model and its variants. If, in addition, they feel a systematic contrarian trend, the result may be a time periodic adjustment of the flock or period doubling in time. This is demonstrated by analyzing a modified Vicsek model of self-propelled particles and its corresponding kinetic equation valid for a large number of particles. We have carried out a stability and bifurcation analysis of the order-disorder transition to spatially uniform stationary or time periodic solutions that are characterized by their complex order parameters. Direct numerical simulations differing from theoretical predictions indicate the formation of spatiotemporal structures. Strikingly, we have found that increasing the usual alignment noise may favor flocking and an optimum noise produces the strongest possible order parameter.Comment: 21 pages, 12 figures, revised versio

Persuasion without polarization? Modelling persuasive argument communication in teams with strong faultlines

Strong demographic faultlines are a potential source of conflict in teams. To study conditions under which faultlines can result in between-group bi-polarization of opinions, a computational model of persuasive argument communication has been proposed. We identify two hitherto overlooked degrees of freedom in how researchers formalized the theory. First, are arguments agents communicate influencing each other's opinions explicitly or implicitly represented in the model? Second, does similarity between agents increase chances of interaction or the persuasiveness of others' arguments? Here we examine these degrees of freedom in order to assess their effect on the model's predictions. We find that both degrees of freedom matter: in a team with strong demographic faultline, the model predicts more between-group bi-polarization when (1) arguments are represented explicitly, and (2) when homophily is modelled such that the interaction between similar agents are more likely (instead of more persuasive)

Modelos de dinámicas de la opinión. Una revisión de la literatura

The study of public opinion is turning in the last years, the study from the traditional descriptive approach with informative and advising purposes to a new explanatory and generativist approach. This new perspective has focused on the construction and analysis of models where local, microscopic, interactions generate macroscopic regularities in public opinion. The fertility of this new approach is causing a publication rhythm that can be overwhelming. In this paper, we present an up to date revision of the literature on opinion dynamics models. We present the main models and their extensions, and organize the exposition around ten axes that configure the content of each contribution. The paper also offers some reflections on the main challenges for those social scientists that are interested in the dynamics of public opinion.El estudio de la opinión pública está girando, en los últimos años, del tradicional enfoque descriptivo con fines informativos y de asesoramiento a un nuevo enfoque explicativo y generativista. Este nuevo enfoque se ha centrado en la construcción y análisis de modelos en los que las interacciones locales, microscópicas, generan las regularidades macroscópicas de la opinión pública. La fertilidad de este nuevo enfoque se está traduciendo en un ritmo de publicaciones que puede llegar a ser abrumador. En este trabajo presentamos una revisión actualizada de la literatura sobre los modelos de dinámicas de la opinión. Se presentan los principales modelos y sus extensiones, organizado la exposición alrededor de diez ejes de debate que configuran el contenido de cada aportación. El artículo ofrece también algunas reflexiones sobre los principales desafíos que tienen ante sí los científicos sociales interesados en el estudio de las dinámicas de la opinión