19 research outputs found
First--order continuous models of opinion formation
We study certain nonlinear continuous models of opinion formation derived
from a kinetic description involving exchange of opinion between individual
agents. These models imply that the only possible final opinions are the
extremal ones, and are similar to models of pure drift in magnetization. Both
analytical and numerical methods allow to recover the final distribution of
opinion between the two extremal ones.Comment: 17 pages, 4 figure
The undecided have the key: Interaction-driven opinion dynamics in a three state model
The effects of interpersonal interactions on individual's agreements result
in a social aggregation process which is reflected in the formation of
collective states, as for instance, groups of individuals with a similar
opinion about a given issue. This field, which has been a longstanding concern
of sociologists and psychologists, has been extended into an area of
experimental social psychology, and even has attracted the attention of
physicists and mathematicians. In this article, we present a novel model of
opinion formation in which agents may either have a strict preference for a
choice, or be undecided. The opinion shift emerges during interpersonal
communications, as a consequence of a cumulative process of conviction for one
of the two extremes opinions through repeated interactions. There are two main
ingredients which play key roles in determining the steady state: the initial
fraction of undecided agents and the conviction's sensitivity in each
interaction. As a function of these two parameters, the model presents a wide
range of possible solutions, as for instance, consensus of each opinion,
bi-polarisation or convergence of undecided individuals. We found that a
minimum fraction of undecided agents is crucial not only for reaching consensus
of a given opinion, but also to determine a dominant opinion in a polarised
situation. In order to gain a deeper comprehension of the dynamics, we also
present the theoretical master equations of the model.Comment: 21 pages, 6 figure
Kinetic description of optimal control problems and applications to opinion consensus
In this paper an optimal control problem for a large system of interacting
agents is considered using a kinetic perspective. As a prototype model we
analyze a microscopic model of opinion formation under constraints. For this
problem a Boltzmann-type equation based on a model predictive control
formulation is introduced and discussed. In particular, the receding horizon
strategy permits to embed the minimization of suitable cost functional into
binary particle interactions. The corresponding Fokker-Planck asymptotic limit
is also derived and explicit expressions of stationary solutions are given.
Several numerical results showing the robustness of the present approach are
finally reported.Comment: 25 pages, 18 figure
Opinion modeling on social media and marketing aspects
We introduce and discuss kinetic models of opinion formation on social
networks in which the distribution function depends on both the opinion and the
connectivity of the agents. The opinion formation model is subsequently coupled
with a kinetic model describing the spreading of popularity of a product on the
web through a social network. Numerical experiments on the underlying kinetic
models show a good qualitative agreement with some measured trends of hashtags
on social media websites and illustrate how companies can take advantage of the
network structure to obtain at best the advertisement of their products
Modelling opinion formation by means of kinetic equations
In this chapter, we review some mechanisms of opinion dynamics that can be modelled by kinetic equations. Beside the sociological phenomenon of compromise, naturally linked to collisional operators of Boltzmann kind, many other aspects, already mentioned in the sociophysical literature or no, can enter in this framework. While describing some contributions appeared in the literature, we enlighten some mathematical tools of kinetic theory that can be useful in the context of sociophysics