Emergence of group hierarchy

TL;DR

This paper studies how group hierarchies naturally form in opinion dynamics models where agents interact randomly, update opinions about each other and others, and are influenced by their group averages, supported by simulations and mathematical analysis.

Contribution

It introduces a new opinion dynamics model with group influence and derives a moment approximation explaining hierarchy emergence.

Findings

Hierarchies emerge from neutral opinions in simulations.

The moment approximation predicts the evolution of inter-group opinions.

Mathematical analysis clarifies the conditions for hierarchy formation.

Abstract

We consider an opinion dynamics model where, during random pair interactions, each agent modifies her opinions about both agents of the random pair and also about some other agents, chosen randomly. Moreover, each agent belongs to a single group and the opinions within the group are attracted to their average. In simulations starting from neutral opinions, we observe the emergence of a group hierarchy. We derive a moment approximation that provides equations ruling the evolution of the average opinion of agents in a group about the agents of another group. This approximation explains how the group hierarchy emerges.