An agent based force vector model of social influence that predicts strong polarization in a connected world

Abstract

The model is based on a vector representation of each agent. The components of the vector are the key continuous “attributes” that determine the social behavior of the agent. A simple mathematical force vector model is used to predict the effect of each agent on all other agents. The force law used is motivated by gravitational force laws and electrical force laws for dipoles. It assumes that the force between two agents is proportional to the “similarity of attributes”, which is implemented mathematically as the dot product of the vectors representing the attributes of the agents, and the force goes as the inverse square of the difference in attributes, which is expressed as the Euclidean distance in attribute space between the two vectors. The force between the agents may be positive (attractive), zero, or negative (repulsive) depending on whether the angle between the corresponding vectors is less than, equal to, or greater than 90°. A positive force causes the attributes of the agents to become more similar and the corresponding vectors to become more nearly parallel. Interaction between all agents is allowed unless the distance between the attributes representing the agents exceeds a confidence limit (the Attribute Influence Bound) set in the simulation. Agents with similar attributes tend to form groups. For small values of the Attribute Influence Bound, numerous groups remain scattered throughout attribute space at the end of a simulation. As the Attribute Influence Bound is increased, and agents with increasingly different attributes can communicate, fewer groups remain at the end, and the remaining groups have increasingly different characteristic attributes and approximately equal sizes. With a large Attribute Influence Bound all agents are connected and extreme bi- or tri-polarization results. During the simulations, depending on the initial conditions, collective behaviors of grouping, consensus, fragmentation and polarization are observed as well as certain symmetries specific to the model, for example, the average of the attributes for all agents does not change significantly during a simulation.