Modeling opinion dynamics: How the network enhances consensus (original) (raw)
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Opinion dynamics over complex networks: Kinetic modelling and numerical methods
Kinetic & Related Models, 2016
In this paper we consider the modeling of opinion dynamics over time dependent large scale networks. A kinetic description of the agents' distribution over the evolving network is considered which combines an opinion update based on binary interactions between agents with a dynamic creation and removal process of new connections. The number of connections of each agent influences the spreading of opinions in the network but also the way connections are created is influenced by the agents' opinion. The evolution of the network of connections is studied by showing that its asymptotic behavior is consistent both with Poisson distributions and truncated power-laws. In order to study the large time behavior of the opinion dynamics a mean field description is derived which allows to compute exact stationary solutions in some simplified situations. Numerical methods which are capable to describe correctly the large time behavior of the system are also introduced and discussed. Finally, several numerical examples showing the influence of the agents' number of connections in the opinion dynamics are reported.
Opinion dynamics over complex networks: kinetic modeling and numerical methods
arXiv (Cornell University), 2016
In this paper we consider the modeling of opinion dynamics over time dependent large scale networks. A kinetic description of the agents' distribution over the evolving network is considered which combines an opinion update based on binary interactions between agents with a dynamic creation and removal process of new connections. The number of connections of each agent influences the spreading of opinions in the network but also the way connections are created is influenced by the agents' opinion. The evolution of the network of connections is studied by showing that its asymptotic behavior is consistent both with Poisson distributions and truncated power-laws. In order to study the large time behavior of the opinion dynamics a mean field description is derived which allows to compute exact stationary solutions in some simplified situations. Numerical methods which are capable to describe correctly the large time behavior of the system are also introduced and discussed. Finally, several numerical examples showing the influence of the agents' number of connections in the opinion dynamics are reported.
Diffusion Controlled Model of Opinion Dynamics
Reports in Advances of Physical Sciences, 2017
We have studied the effect of diffusion controlled opinion dynamics on a ring lattice where agents are placed on a fraction of sites. We have chosen the diffusion on a circular ring as a simple model to study emphasizing on the fact that agents approach their nearest neighbor for exchanging opinion. The agents execute simple exclusion process (SEP) on the ring and exchange opinion with neighboring agents according to a fixed rule. Our study shows that as agent density decreases, higher conviction power is necessary to create consensus. We have also investigated the nature of active-to-absorbing state phase transition for various densities and found that there are two universality classes for density [Formula: see text] and [Formula: see text].
Mathematical Modeling of Collective Behavior in Socio-Economic and Life Sciences, 2010
In this chapter, we briefly review some opinion dynamics models starting from the classical Schelling model and other agent-based modelling examples. We consider both discrete and continuous models and we briefly describe different approaches: discrete dynamical systems and agent-based models, partial differential equations based models, kinetic framework. We also synthesized some comparisons between different methods with the main references in order to further analysis and remarks.
Anti-diffusion in continuous opinion dynamics
Physica A: Statistical Mechanics and its Applications
Considerable effort using techniques developed in statistical physics has been aimed at numerical simulations of agent-based opinion models and analysis of their results. Such work has elucidated how various rules for interacting agents can give rise to steady state behaviors in the agent populations that vary between consensus and fragmentation. At the macroscopic population level, analysis has been limited due to the lack of an analytically tractable governing macro-equation for the continuous population state. We use the integro-differential equation that governs opinion dynamics for the continuous probability distribution function of agent opinions to develop a novel nonlinear partial differential equation for the evolution of opinion distributions. The highly nonlinear equation allows for the generation of a system of approximations. We consider three initial population distributions and determine their small-time behavior. Our analysis reveals how the generation of clusters results from the interplay of diffusion and anti-diffusion and how initial instabilities arise in different regions of the population distribution.
Modelling collective opinion formation by means of active Brownian particles
The European Physical Journal B, 2000
The concept of active Brownian particles is used to model a collective opinion formation process. It is assumed that individuals in community create a two-component communication field that influences the change of opinions of other persons and/or can induce their migration. The communication field is described by a reaction-diffusion equation, the opinion change of the individuals is given by a master equation, while the migration is described by a set of Langevin equations, coupled by the communication field. In the mean-field limit holding for fast communication we derive a critical population size, above which the community separates into a majority and a minority with opposite opinions. The existence of external support (e.g. from mass media) changes the ratio between minority and majority, until above a critical external support the supported subpopulation exists always as a majority. Spatial effects lead to two critical "social" temperatures, between which the community exists in a metastable state, thus fluctuations below a certain critical wave number may result in a spatial opinion separation. The range of metastability is particularly determined by a parameter characterizing the individual response to the communication field. In our discussion, we draw analogies to phase transitions in physical systems.
A population dynamics model for opinion dynamics with prominent agents and incentives
2013 American Control Conference, 2013
In this paper, the design of a population dynamics model based on both opinion and imitator dynamics is presented. This approach is focused on the analysis of some population behaviors such as the emergence of either consensus or disagreement, information aggregation, and spread of misinformation. The analysis of these properties is made in the context of network populations with or without the presence of prominent agents and environmental incentives. Some simulation results illustrate the ideas presented in this paper.
Vector opinion dynamics in a model for social influence
Physica A: Statistical Mechanics and its Applications, 2003
We present numerical simulations of a model of social influence, where the opinion of each agent is represented by a binary vector. Agents adjust their opinions as a result of random encounters, whenever the difference between opinions is below a given threshold. Evolution leads to a steady state, which highly depends on the threshold and a convergence parameter of the model. We analyze the transition between clustered and homogeneous steady states. Results of the cases of complete mixing and small-world networks are compared.