4,183 research outputs found
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
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
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
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
On the Steady State of Continuous Time Stochastic Opinion Dynamics with Power Law Confidence
This paper introduces a class of non-linear and continuous-time opinion
dynamics model with additive noise and state dependent interaction rates
between agents. The model features interaction rates which are proportional to
a negative power of opinion distances. We establish a non-local partial
differential equation for the distribution of opinion distances and use Mellin
transforms to provide an explicit formula for the stationary solution of the
latter, when it exists. Our approach leads to new qualitative and quantitative
results on this type of dynamics. To the best of our knowledge these Mellin
transform results are the first quantitative results on the equilibria of
opinion dynamics with distance-dependent interaction rates. The closed form
expressions for this class of dynamics are obtained for the two agent case.
However the results can be used in mean-field models featuring several agents
whose interaction rates depend on the empirical average of their opinions. The
technique also applies to linear dynamics, namely with a constant interaction
rate, on an interaction graph
Social Influence of Competing Groups and Leaders in Opinion Dynamics
Publication history: Accepted - 11 September 2020; Published online - 19 September 2020.This paper explores the infuence of two competing stubborn agent groups on the
opinion dynamics of normal agents. Computer simulations are used to investigate
the parameter space systematically in order to determine the impact of group size
and extremeness on the dynamics and identify optimal strategies for maximizing
numbers of followers and social infuence. Results show that (a) there are many
cases where a group that is neither too large nor too small and neither too extreme
nor too central achieves the best outcome, (b) stubborn groups can have a moderating, rather than polarizing, efect on the society in a range of circumstances, and (c)
small changes in parameters can lead to transitions from a state where one stubborn
group attracts all the normal agents to a state where the other group does so. We also
explore how these fndings can be interpreted in terms of opinion leaders, truth, and
campaign
- …