Stochastic dynamics of self-organizing social systems with memory (electoral processes)

The paper discusses the use of the methods and approaches which are common for theoretical computer science as well as the use of its applications for analysis and modeling of social group processes. Based on the developed model for describing stochastic processes, taking into account self-organization and the presence of memory, an analysis of the voter preference dynamics during the 2016 U.S. presidential campaign was conducted. The sociological data processing allowed plotting the probability density histograms for the amplitudes of voter preference deviation, depending on their determination interval, and developing a model that well describes the main characteristics of the observed processes (appearance of oscillations, changes in the height and width of the distribution depending on the changes in the amplitude calculation interval, etc.). In the course of building the model, the probability schemes of transitions between the possible states of the social system (voter preferences) were considered and a second-order nonlinear differential equation was derived. In addition, a boundary problem to determine the probability density function of the amplitude of voter preference deviation depending on its determination interval was formulated and solved. The model differential equation has a term responsible for the self-organization possibility and takes into account the presence of memory. The oscillation possibility depends on the initial conditions. The developed model can be used for analyzing election campaigns and making relevant decisions.