A Mathematical Model for the Behavior of Individuals in a Social Field

TL;DR

This paper introduces a mathematical model describing how individual behaviors change under social influences, incorporating social norms, trends, and interaction processes like imitation and avoidance.

Contribution

It develops a novel mathematical framework that captures the effects of social fields and individual interactions on behavior change.

Findings

Model successfully integrates social norms and individual interactions.

Differentiates between imitative and avoidance behaviors.

Provides a basis for analyzing social influence dynamics.

Abstract

Related to an idea of Lewin, a mathematical model for behavioral changes under the influence of a social field is developed. The social field reflects public opinion, social norms and trends. It is not only given by external factors (the environment) but also by the interactions of individuals. Two important kinds of interaction processes are distinguished: Imitative and avoidance processes. Variations of individual behavior are taken into account by ``diffusion coefficients''.