Mathematical Model of Opinion Dynamics in Social Groups

Abstract

Mathematical models describing relationships in a group of individuals are known for a long time. The basic idea underlying these models can be described as follows. There are affective (emotionally colored) not necessarily symmetrical relationships between any two members of the group. In general, these relationships vary over time and can be described by numerical functions of time. The value of the corresponding function is positive if the first individual has a positive attitude toward the second one and negative if the attitude is negative. While interacting, two individuals share their views on other members of the group. It affects the dynamics of group relationships. At the same time, the model uses principles such as “if the person whom I dislike says something unpleasant about a third person then I improve my opinion of this third person.” This paper also deals with the modeling of group interactions, with the difference that the considered interactions have features of mass (not paired) communications, i.e., the opinion of each individual is equally available to all the others (at the same time, affective relations are paired). This situation occurs, for example, in communities of users of internet forums and blogging platforms. Another important difference is due to the fact that individuals do not discuss other members of the group, but discuss various issues on the topic (e.g., political) of interest to all members of the group. The results of numerical experiments for the system are presented and a number of substantial conclusions are formulated.

DOI: 10.5901/mjss.2013.v4n10p380