Opinion modeling on social media and marketing aspects

Kinetic Models for Epidemic Dynamics in the Presence of Opinion Polarization

Understanding the impact of collective social phenomena in epidemic dynamics is a crucial task to effectively contain the disease spread. In this work, we build a mathematical description for assessing the interplay between opinion polarization and the evolution of a disease. The proposed kinetic approach describes the evolution of aggregate quantities characterizing the agents belonging to epidemiologically relevant states and will show that the spread of the disease is closely related to consensus dynamics distribution in which opinion polarization may emerge. In the present modelling framework, microscopic consensus formation dynamics can be linked to macroscopic epidemic trends to trigger the collective adherence to protective measures. We conduct numerical investigations which confirm the ability of the model to describe different phenomena related to the spread of an epidemic.

Opinion Polarization in Human Communities Can Emerge as a Natural Consequence of Beliefs Being Interrelated

The emergence of opinion polarization within human communities-the phenomenon that individuals within a society tend to develop conflicting attitudes related to the greatest diversity of topics-has been a focus of interest for decades, both from theoretical and modelling points of view. Regarding modelling attempts, an entire scientific field-opinion dynamics-has emerged in order to study this and related phenomena. Within this framework, agents' opinions are usually represented by a scalar value which undergoes modification due to interaction with other agents. Under certain conditions, these models are able to reproduce polarization-a state increasingly familiar to our everyday experience. In the present paper, an alternative explanation is suggested along with its corresponding model. More specifically, we demonstrate that by incorporating the following two well-known human characteristics into the representation of agents: (1) in the human brain beliefs are interconnected, and (2) people strive to maintain a coherent belief system; polarization immediately occurs under exposure to news and information. Furthermore, the model accounts for the proliferation of fake news, and shows how opinion polarization is related to various cognitive biases.

Opinion polarization in social networks

In this paper, we propose a Boltzmann-type kinetic description of opinion formation on social networks, which takes into account a general connectivity distribution of the individuals. We consider opinion exchange processes inspired by the Sznajd model and related simplifications but we do not assume that individuals interact on a regular lattice. Instead, we describe the structure of the social network statistically, assuming that the number of contacts of a given individual determines the probability that their opinion reaches and influences the opinion of another individual. From the kinetic description of the system, we study the evolution of the mean opinion, whence we find precise analytical conditions under which a polarization switch of the opinions, i.e. a change of sign between the initial and the asymptotic mean opinions, occurs. In particular, we show that a non-zero correlation between the initial opinions and the connectivity of the individuals is necessary to observe polarization switch. Finally, we validate our analytical results through Monte Carlo simulations of the stochastic opinion exchange processes on the social network. This article is part of the theme issue 'Kinetic exchange models of societies and economies'.

On a kinetic opinion formation model for pre-election polling

Motivated by recent successes in model-based pre-election polling, we propose a kinetic model for opinion formation which includes voter demographics and socio-economic factors like age, sex, ethnicity, education level, income and other measurable factors like behaviour in previous elections or referenda as a key driver in the opinion formation dynamics. The model is based on Toscani's kinetic opinion formation model (Toscani G. 2006 Kinetic models of opinion formation. Commun. Math. Sci. 4, 481-496.) and the leader-follower model of Düring et al. (Düring B. et al. 2009 Boltzmann and Fokker-Planck equations modelling opinion formation in the presence of strong leaders. Proc. R. Soc. A 465, 3687-3708.), and leads to a system of coupled Boltzmann-type equations and associated, approximate Fokker-Planck-type systems. Numerical examples using data from general elections in the UK show the effect different demographics have on the opinion formation process and the outcome of elections. This article is part of the theme issue 'Kinetic exchange models of societies and economies'.

From agent-based models to the macroscopic description of fake-news spread: the role of competence in data-driven applications

Fake news spreading, with the aim of manipulating individuals' perceptions of facts, is now recognized as a major problem in many democratic societies. Yet, to date, little has been understood about how fake news spreads on social networks, what the influence of the education level of individuals is, when fake news is effective in influencing public opinion, and what interventions might be successful in mitigating their effect. In this paper, starting from the recently introduced kinetic multi-agent model with competence by the first two authors, we propose to derive reduced-order models through the notion of social closure in the mean-field approximation that has its roots in the classical hydrodynamic closure of kinetic theory. This approach allows to obtain simplified models in which the competence and learning of the agents maintain their role in the dynamics and, at the same time, the structure of such models is more suitable to be interfaced with data-driven applications. Examples of different Twitter-based test cases are described and discussed.

On Systems of Active Particles Perturbed by Symmetric Bounded Noises: A Multiscale Kinetic Approach

We consider an ensemble of active particles, i.e., of agents endowed by internal variables u(t). Namely, we assume that the nonlinear dynamics of u is perturbed by realistic bounded symmetric stochastic perturbations acting nonlinearly or linearly. In the absence of birth, death and interactions of the agents (BDIA) the system evolution is ruled by a multidimensional Hypo-Elliptical Fokker–Plank Equation (HEFPE). In presence of nonlocal BDIA, the resulting family of models is thus a Partial Integro-differential Equation with hypo-elliptical terms. In the numerical simulations we focus on a simple case where the unperturbed dynamics of the agents is of logistic type and the bounded perturbations are of the Doering–Cai–Lin noise or the Arctan bounded noise. We then find the evolution and the steady state of the HEFPE. The steady state density is, in some cases, multimodal due to noise-induced transitions. Then we assume the steady state density as the initial condition for the full system evolution. Namely we modeled the vital dynamics of the agents as logistic nonlocal, as it depends on the whole size of the population. Our simulations suggest that both the steady states density and the total population size strongly depends on the type of bounded noise. Phenomena as transitions to bimodality and to asymmetry also occur.

Opinion Formation on the Internet: The Influence of Personality, Network Structure, and Content on Sharing Messages Online

Today the majority of people uses online social networks not only to stay in contact with friends, but also to find information about relevant topics, or to spread information. While a lot of research has been conducted into opinion formation, only little is known about which factors influence whether a user of online social networks disseminates information or not. To answer this question, we created an agent-based model and simulated message spreading in social networks using a latent-process model. In our model, we varied four different content types, six different network types, and we varied between a model that includes a personality model for its agents and one that did not. We found that the network type has only a weak influence on the distribution of content, whereas the message type has a clear influence on how many users receive a message. Using a personality model helped achieved more realistic outcomes.

Economic Segregation Under the Action of Trading Uncertainties

We study the distribution of wealth in a market economy in which the trading propensity of the agents is uncertain. Our approach is based on kinetic models for collective phenomena, which, at variance with the classical kinetic theory of rarefied gases, has to face the lack of fundamental principles, which are replaced by empirical social forces of which we have at most statistical information. The proposed kinetic description allows recovering emergent wealth distribution profiles, which are described by the steady states of a Fokker–Planck-type equation with uncertain parameters. A statistical study of the stationary profiles of the Fokker–Planck equation then shows that the wealth distribution can develop a multimodal shape in the presence of observable highly stressful economic situations.

Conservative discrete-velocity method for the ellipsoidal Fokker-Planck equation in gas-kinetic theory

A conservative discrete velocity method (DVM) is developed for the ellipsoidal Fokker-Planck (ES-FP) equation in prediction of nonequilibrium neutral gas flows in this paper. The ES-FP collision operator is solved in discrete velocity space in a concise and quick finite difference framework. The conservation problem of the discrete ES-FP collision operator is solved by multiplying each term in it by extra conservative coefficients whose values are very close to unity. Their differences to unity are in the same order of the numerical error in approximating the ES-FP operator in discrete velocity space. All the macroscopic conservative variables (mass, momentum, and energy) are conserved in the present modified discrete ES-FP collision operator. Since the conservation property in a discrete element of physical space is very important for the numerical scheme when discontinuity and a large gradient exist in the flow field, a finite volume framework is adopted for the transport term of the ES-FP equation. For nD-3V (n<3) cases, a nD-quasi nV reduction is specifically proposed for the ES-FP equation and the corresponding FP-DVM method, which can greatly reduce the computational cost. The validity and accuracy of both the ES-FP equation and FP-DVM method are examined using a series of 0D-3V homogenous relaxation cases and 1D-3V shock structure cases with different Mach numbers, in which 1D-3V cases are reduced to 1D-quasi 1V cases. Both the predictions of 0D-3V and 1D-3V cases match well with the benchmark results such as the analytical Boltzmann solution, direct full-Boltzmann numerical solution, and DSMC result. Especially, the FP-DVM predictions match well with the DSMC results in the Mach 8.0 shock structure case, which is in high nonequilibrium, and is a challenge case of the model Boltzmann equation and the corresponding numerical methods.

Multiple-interaction kinetic modeling of a virtual-item gambling economy

In recent years, there has been a proliferation of online gambling sites, which has made gambling more accessible with a consequent rise in related problems, such as addiction. Hence, the analysis of the gambling behavior at both the individual and the aggregate levels has become the object of several investigations. In this paper, resorting to classical methods of the kinetic theory, we describe the behavior of a multiagent system of gamblers participating in lottery-type games on a virtual-item gambling market. The comparison with previous, often empirical, results highlights the ability of the kinetic approach to explain how the simple microscopic rules of a gambling-type game produce complex collective trends, which might be difficult to interpret precisely by looking only at the available data.