Novel Multidimensional Models of Opinion Dynamics in Social Networks

Unlike many complex networks studied in the literature, social networks rarely exhibit unanimous behavior, or consensus. This requires a development of mathematical models that are sufficiently simple to be examined and capture, at the same time, the complex behavior of real social groups, where opinions and actions related to them may form clusters of different size. One such model, proposed by Friedkin and Johnsen, extends the idea of conventional consensus algorithm (also referred to as the iterative opinion pooling) to take into account the actors' prejudices, caused by some exogenous factors and leading to disagreement in the final opinions. In this paper, we offer a novel multidimensional extension, describing the evolution of the agents' opinions on several topics. Unlike the existing models, these topics are interdependent, and hence the opinions being formed on these topics are also mutually dependent. We rigorous examine stability properties of the proposed model, in particular, convergence of the agents' opinions. Although our model assumes synchronous communication among the agents, we show that the same final opinions may be reached "on average" via asynchronous gossip-based protocols.Comment: Accepted by IEEE Transaction on Automatic Control (to be published in May 2017

シャカイネットワークニオケルオピニオンダイナミクスノゴシップベースモデル

Emerico Aguilar & Yasumasa Fujisaki. "Reaching consensus via coordinated groups", SICE Journal of Control, Measurement, and System Integration, 14(1), 20-26 (2021). DOI: 10.1080/18824889.2021.1874673

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

Detecting Communities in a Gossip Model with Stubborn Agents

We consider a community detection problem for a gossip model, in which agents randomly interact pairwise, and there are stubborn agents never changing their states. Such a model can illustrate how disagreement and opinion fluctuation arise in a social network. It is assumed that each agent is assigned with one of the two community labels, and the agents interact with probabilities depending on their labels. The considered problem is twofold: to infer the community labels of agents, and to estimate interaction probabilities between the agents, based on a single trajectory of the model. We first study stability and limit theorems of the model, and then propose a joint detection and estimation algorithm based on agent states. It is verified that the community detector of the algorithm converges in finite time, and the interaction estimator converges almost surely. We derive a sample-complexity result for successful community detection, and analyze convergence rate of the interaction estimator. Simulations are presented for illustration of the performance of the proposed algorithm

Dynamical Networks of Social Influence: Modern Trends and Perspectives

Dynamics and control of processes over social networks, such as the evolution of opinions, social influence and interpersonal appraisals, diffusion of information and misinformation, emergence and dissociation of communities, are now attracting significant attention from the broad research community that works on systems, control, identification and learning. To provide an introduction to this rapidly developing area, a Tutorial Session was included into the program of IFAC World Congress 2020. This paper provides a brief summary of the three tutorial lectures, covering the most “mature” directions in analysis of social networks and dynamics over them: 1) formation of opinions under social influence; 2) identification and learning for analysis of a network’s structure; 3) dynamics of interpersonal appraisals

Learning Hidden Influences in Large-Scale Dynamical Social Networks: A Data-Driven Sparsity-Based Approach, in Memory of Roberto Tempo

The processes of information diffusion across social networks (for example, the spread of opinions and the formation of beliefs) are attracting substantial interest in disciplines ranging from behavioral sciences to mathematics and engineering (see "Summary"). Since the opinions and behaviors of each individual are infl uenced by interactions with others, understanding the structure of interpersonal infl uences is a key ingredient to predict, analyze, and, possibly, control information and decisions [1]. With the rapid proliferation of social media platforms that provide instant messaging, blogging, and other networking services (see "Online Social Networks") people can easily share news, opinions, and preferences. Information can reach a broad audience much faster than before, and opinion mining and sentiment analysis are becoming key challenges in modern society [2]. The first anecdotal evidence of this fact is probably the use that the Obama campaign made of social networks during the 2008 U.S. presidential election [3]. More recently, several news outlets stated that Facebook users played a major role in spreading fake news that might have infl uenced the outcome of the 2016 U.S. presidential election [4]. This can be explained by the phenomena of homophily and biased assimilation [5]-[7] in social networks, which correspond to the tendency of people to follow the behaviors of their friends and establish relationships with like-minded individuals

How Realistic Should Knowledge Diffusion Models Be?

Knowledge diffusion models typically involve two main features: an underlying social network topology on one side, and a particular design of interaction rules driving knowledge transmission on the other side. Acknowledging the need for realistic topologies and adoption behaviors backed by empirical measurements, it becomes unclear how accurately existing models render real-world phenomena: if indeed both topology and transmission mechanisms have a key impact on these phenomena, to which extent does the use of more or less stylized assumptions affect modeling results? In order to evaluate various classical topologies and mechanisms, we push the comparison to more empirical benchmarks: real-world network structures and empirically measured mechanisms. Special attention is paid to appraising the discrepancy between diffusion phenomena (i) on some real network topologies vs. various kinds of scale-free networks, and (ii) using an empirically-measured transmission mechanism, compared with canonical appropriate models such as threshold models. We find very sensible differences between the more realistic settings and their traditional stylized counterparts. On the whole, our point is thus also epistemological by insisting that models should be tested against simulation-based empirical benchmarks.Agent-Based Simulation, Complex Systems, Empirical Calibration and Validation, Knowledge Diffusion, Model Comparison, Social Networks

Resilient Consensus for Robust Multiplex Networks with Asymmetric Confidence Intervals

The consensus problem with asymmetric confidence intervals considered in this paper is characterized by the fact that each agent can have optimistic and/or pessimistic interactions with its neighbors. To deal with the asymmetric confidence scenarios, we introduce a novel multiplex network presentation for directed graphs and its associated connectivity concepts including the pseudo-strongly connectivity and graph robustness, which provide a resilience characterization in the presence of malicious nodes. We develop distributed resilient consensus strategies for a group of dynamical agents with locally bounded Byzantine agents in both continuous-time and discrete-time multi-agent systems. Drawing on our multiplex network framework, much milder connectivity conditions compared to existing works are proposed to ensure resilient consensus. The results are further extended to cope with resilient scaled consensus problems which allow both cooperative and antagonistic agreements among agents. Numerical examples are also exhibited to confirm the theoretical results and reveal the factors that affect the speed of convergence in our multiplex network framework