Consensus in the Presence of Multiple Opinion Leaders: Effect of Bounded Confidence

The problem of analyzing the performance of networked agents exchanging evidence in a dynamic network has recently grown in importance. This problem has relevance in signal and data fusion network applications and in studying opinion and consensus dynamics in social networks. Due to its capability of handling a wider variety of uncertainties and ambiguities associated with evidence, we use the framework of Dempster-Shafer (DS) theory to capture the opinion of an agent. We then examine the consensus among agents in dynamic networks in which an agent can utilize either a cautious or receptive updating strategy. In particular, we examine the case of bounded confidence updating where an agent exchanges its opinion only with neighboring nodes possessing 'similar' evidence. In a fusion network, this captures the case in which nodes only update their state based on evidence consistent with the node's own evidence. In opinion dynamics, this captures the notions of Social Judgment Theory (SJT) in which agents update their opinions only with other agents possessing opinions closer to their own. Focusing on the two special DS theoretic cases where an agent state is modeled as a Dirichlet body of evidence and a probability mass function (p.m.f.), we utilize results from matrix theory, graph theory, and networks to prove the existence of consensus agent states in several time-varying network cases of interest. For example, we show the existence of a consensus in which a subset of network nodes achieves a consensus that is adopted by follower network nodes. Of particular interest is the case of multiple opinion leaders, where we show that the agents do not reach a consensus in general, but rather converge to 'opinion clusters'. Simulation results are provided to illustrate the main results.Comment: IEEE Transactions on Signal and Information Processing Over Networks, to appea

Bounded Rationality, Social Learning and Collective Behavior: Decisional Analysis in a Nested World

People are usually brought together in a social network to make synergetic decisions. This decision making process often involves information acquisition and social learning, which are essential to overcome individuals’ bounded rationality. The performance of a society thus depends on the collective behavior of individuals. Besides information attributes, organizational properties often influenced such a decision process. In this article, we introduce a paradigm -- nested world -- that treats social network as a symbolic system. Based on this paradigm, we developed a research model to investigate how information attributes, social parameters, and their interactions influenced the performance of a social network. This research model was subsequently converted to a computational model for analysis and validation. Our findings suggested that informativeness, network density, social influence, and their interactions had significant influence on the performance of whole society. Besides these findigns, many interesting phenomenon were also observed, including significant social learning curve, U-shape decision speed, threshold of network density, and interchangeability between network density and social influence

Belief Dynamics in Social Networks: A Fluid-Based Analysis

The advent and proliferation of social media have led to the development of mathematical models describing the evolution of beliefs/opinions in an ecosystem composed of socially interacting users. The goal is to gain insights into collective dominant social beliefs and into the impact of different components of the system, such as users' interactions, while being able to predict users' opinions. Following this thread, in this paper we consider a fairly general dynamical model of social interactions, which captures all the main features exhibited by a social system. For such model, by embracing a mean-field approach, we derive a diffusion differential equation that represents asymptotic belief dynamics, as the number of users grows large. We then analyze the steady-state behavior as well as the time dependent (transient) behavior of the system. In particular, for the steady-state distribution, we obtain simple closed-form expressions for a relevant class of systems, while we propose efficient semi-analytical techniques in the most general cases. At last, we develop an efficient semi-analytical method to analyze the dynamics of the users' belief over time, which can be applied to a remarkably large class of systems.Comment: submitted to IEEE TNS

Effect of Stubborn Agents on Bounded Confidence Opinion Dynamic Systems: Unanimity in Presence of Stubborn Agents

In this paper, various bounded confidence opinion dynamic algorithms are examined to illustrate the effect of a stubborn minority groups on opinion dynamics. A notion of variable opinion stubborn agent is defined and it is shown that stubborn minorities are able to fully control the opinions of a Hegselmann-Krause opinion dynamic system through deliberate slow variation in the opinions of stubborn agents. Furthermore, an upper bound for the change rate of stubborn agents to preserve connectivity and control other flexible agents is given. Moreover, a method based on population and growing confidence bound is presented to achieve both unanimity and stubborn opinion rejection. To support the proposed method simulation results are provided