Opinion fluctuations and disagreement in social networks

We study a tractable opinion dynamics model that generates long-run disagreements and persistent opinion fluctuations. Our model involves an inhomogeneous stochastic gossip process of continuous opinion dynamics in a society consisting of two types of agents: regular agents, who update their beliefs according to information that they receive from their social neighbors; and stubborn agents, who never update their opinions. When the society contains stubborn agents with different opinions, the belief dynamics never lead to a consensus (among the regular agents). Instead, beliefs in the society fail to converge almost surely, the belief profile keeps on fluctuating in an ergodic fashion, and it converges in law to a non-degenerate random vector. The structure of the network and the location of the stubborn agents within it shape the opinion dynamics. The expected belief vector evolves according to an ordinary differential equation coinciding with the Kolmogorov backward equation of a continuous-time Markov chain with absorbing states corresponding to the stubborn agents and converges to a harmonic vector, with every regular agent's value being the weighted average of its neighbors' values, and boundary conditions corresponding to the stubborn agents'. Expected cross-products of the agents' beliefs allow for a similar characterization in terms of coupled Markov chains on the network. We prove that, in large-scale societies which are highly fluid, meaning that the product of the mixing time of the Markov chain on the graph describing the social network and the relative size of the linkages to stubborn agents vanishes as the population size grows large, a condition of \emph{homogeneous influence} emerges, whereby the stationary beliefs' marginal distributions of most of the regular agents have approximately equal first and second moments.Comment: 33 pages, accepted for publication in Mathematics of Operation Researc

Opinion Polarization by Learning from Social Feedback

We explore a new mechanism to explain polarization phenomena in opinion dynamics in which agents evaluate alternative views on the basis of the social feedback obtained on expressing them. High support of the favored opinion in the social environment, is treated as a positive feedback which reinforces the value associated to this opinion. In connected networks of sufficiently high modularity, different groups of agents can form strong convictions of competing opinions. Linking the social feedback process to standard equilibrium concepts we analytically characterize sufficient conditions for the stability of bi-polarization. While previous models have emphasized the polarization effects of deliberative argument-based communication, our model highlights an affective experience-based route to polarization, without assumptions about negative influence or bounded confidence.Comment: Presented at the Social Simulation Conference (Dublin 2017

Multi-agent decision-making dynamics inspired by honeybees

When choosing between candidate nest sites, a honeybee swarm reliably chooses the most valuable site and even when faced with the choice between near-equal value sites, it makes highly efficient decisions. Value-sensitive decision-making is enabled by a distributed social effort among the honeybees, and it leads to decision-making dynamics of the swarm that are remarkably robust to perturbation and adaptive to change. To explore and generalize these features to other networks, we design distributed multi-agent network dynamics that exhibit a pitchfork bifurcation, ubiquitous in biological models of decision-making. Using tools of nonlinear dynamics we show how the designed agent-based dynamics recover the high performing value-sensitive decision-making of the honeybees and rigorously connect investigation of mechanisms of animal group decision-making to systematic, bio-inspired control of multi-agent network systems. We further present a distributed adaptive bifurcation control law and prove how it enhances the network decision-making performance beyond that observed in swarms

Opinion Fluctuations and Disagreement in Social Network

We study a stochastic gossip model of continuous opinion dynamics in a society consisting of two types of agents: regular agents, who update their beliefs according to information that they receive from their social neighbors; and stubborn agents, who never update their opinions and might represent leaders, political parties or media sources attempting to influence the beliefs in the rest of the society. When the society contains stubborn agents with different opinions, opinion dynamics never lead to a consensus (among the regular agents). Instead, beliefs in the society almost surely fail to converge, and the belief of each regular agent converges in law to a non-degenerate random variable. The model thus generates long-run disagreement and continuous opinion fluctuations. The structure of the social network and the location of stubborn agents within it shape opinion dynamics. When the society is “highly fluid,” meaning that the mixing time of the random walk on the graph describing the social network is small relative to (the inverse of) the relative size of the linkages to stubborn agents, the ergodic beliefs of most of the agents concentrate around a certain common value. We also show that under additional conditions, the ergodic beliefs distribution becomes “approximately chaotic”, meaning that the variance of the aggregate belief of the society vanishes in the large population limit while individual opinions still fluctuate significantly

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