Outline of a Generalization of Kinetic Theory to Study Opinion Dynamics

This paper presents an analytic framework to study the dynamics of the opinion in multi-agent systems. In the proposed framework, each agent is associated with an attribute which represents its opinion, and the opinion of an agent changes because of interactions with other agents, without supervised coordination. Each interaction involves only two agents, and it corresponds to an exchange of messages. The framework assumes that time is modeled as a sequence of discrete steps, which do not necessarily have the same duration, and that at each step two random agents interact. Various sociological phenomena can be incorporated in the proposed framework, and the framework allows studying macroscopic properties of a system starting from microscopic models of such phenomena, obtaining analytic results. In detail, the proposed framework is inspired by the kinetic theory of gas mixtures, which relies on the use of balance equations that can be properly adopted to study opinion dynamics in a multi-agent system. After a short introduction on the kinetic theory of gas mixtures, this paper shows how the main ideas behind it can be generalized to study the dynamics of the opinion in multi-agent systems starting from a detailed description of microscopic interactions among agents.