Discerning media bias within a network of political allies and opponents: Disruption by partisans

An individual's opinions about media bias derive from their own independent assessment of media outputs combined with peer pressure from networked political allies and opponents. Here we generalize previous idealized, probabilistic models of the perception formation process, based on a network of Bayesian learners inferring the bias of a coin, by introducing obdurate agents (partisans), whose opinions stay fixed. It is found that even one partisan destabilizes an allies-only network, stopping it from achieving asymptotic learning and forcing persuadable agents to vacillate indefinitely (turbulent nonconvergence) between the true coin bias $\theta_0$ and the partisan's belief $\theta_{\rm p}$. The dwell time $t_{\rm d}$ at the partisan's belief increases, as the partisan fraction $f$ increases, and decreases, when multiple partisans disagree amongst themselves. In opponents-only networks, asymptotic learning occurs, whether or not partisans are present. However, the counterintuitive tendency to reach wrong conclusions first, identified in previous work with zero partisans, does not persist in general for $\theta_0 \neq \theta_{\rm p}$ in complete networks; it is a property of sparsely connected systems (e.g.\ Barab\'{a}si-Albert networks with attachment parameter $\lesssim 10$). In mixed networks containing allies and opponents, partisans drive counterintuitive outcomes, which depend sensitively, on where they reside. A strongly balanced triad exhibits intermittency with a partisan (sudden transitions between long intervals of static beliefs and turbulent nonconvergence) and asymptotic learning without a partisan.Comment: 36 pages, 17 figure

Perturbed Anisotropic Opinion Dynamics with Delayed Information

We revisited the problem of modeling a publicity campaign in a society of intelligent agents that form their opinions by interchanging information with each other and with the society as a whole. We use a Markov approximation to consider the effects of an interaction delay τ in the system of perturbed differential equations that model the social dynamics. The stable points of the dynamical system are the manifestation of the agent’s attitudes, either in favor or against the social rule, as it was previously found, but the approach to the stable points is greatly modified by the presence of the delay

Opinion Dynamics with Bayesian Learning

Bayesian learning is a rational and effective strategy in the opinion dynamic process. In this paper, we theoretically prove that individual Bayesian learning can realize asymptotic learning and we test it by simulations on the Zachary network. Then, we propose a Bayesian social learning model with signal update strategy and apply the model on the Zachary network to observe opinion dynamics. Finally, we contrast the two learning strategies and find that Bayesian social learning can lead to asymptotic learning more faster than individual Bayesian learning