Kinetic models of opinion formation

Abstract

Abstract. We introduce and discuss certain kinetic models of (continuous) opinion formation involving both exchange of opinion between individual agents and diffusion of information. We show conditions which ensure that the kinetic model reaches non trivial stationary states in case of lack of diffusion in correspondence of some opinion point. Analytical results are then obtained by considering a suitable asymptotic limit of the model yielding a Fokker-Planck equation for the distribution of opinion among individuals.

Recent Advances in Opinion Modeling: Control and Social Influence

“…Observe that the computation of the relative distance between opinions |w − w * | is equivalent to (1.2), since the subtraction cancels the control terms out, giving the inequality 19) which tells that the relative distance in opinion between two agents diminishes after each interaction [99]. In presence of noise terms, we should assure that the binary dynamics (2.16) preserves the boundary, i.e.…”

“…This corresponds to the natural idea that extreme opinions are more difficult to change. Various realizations of these functions can be found in [89,99]. In all cases, however, we assume that both P (w, w * ) and D(w) are non-increasing with respect to |w|, and in addition 0 ≤ P (w, w * ) ≤ 1, 0 ≤ D(w) ≤ 1.…”

“…A similar analysis can be performed for the second moment ϕ(w) = w 2 , showing the decay of the energy for particular choices of the interaction potential (cf. [99,6,7] for further details on the proprieties of the moment of (1.4)).…”

“…The main idea is to scale interaction frequency and strength, λ and η respectively, diffusion ς 2 at the same time, in order to maintain at any level of scaling the memory of the microscopic interactions (2.16). This approach is refereed to as quasi-invariant opinion limit [99,62,102]. Given ε > 0, we consider the following scaling…”

“…From a microscopic viewpoint, the binary interactions in [99] were described by the rules w = w − ηP (w, w * )(w − w * ) + ξD(w), w * = w * − ηP (w * , w)(w * − w) + ξ * D(w * ).…”