Fractal Social Dynamics as a Driver of Consensus and Inequality

TL;DR

This paper models hierarchical social networks using fractal structures and $q$-calculus to understand how consensus forms and inequalities emerge, revealing universal power-law behaviors and heavy-tailed distributions.

Contribution

It introduces a fractal network model combined with $q$-calculus to analyze social dynamics, highlighting the fractal structure's role in consensus and inequality formation.

Findings

Heavy-tailed $q$-Gaussian distributions in the model

Hierarchical fractal structures influence information spread

Inequalities are linked to fractal network properties

Abstract

Human social behavior is organized in stratified, hierarchical networks, with a support group with about 5 members, expanding proportionally at each layer up to a maximum of approximately 150 frequent interactions per individual. This is known as Social Brain Hypothesis, and its findings are supported by psychological and neurological evidence. The fractal network framework provides valuable insights into social phenomena such as the spread of fake news and the development of technology. This study models socioeconomic interactions using fractal networks, where group sizes scale by a fixed factor, to analyze how consensus is formed. Using $q$-calculus, the model reveals how hierarchical structures influence information spread, highlighting universal features governed by power laws.. The results follow $q$-Gaussian distributions, showing heavy-tails that align with observed inequalities in societies worldwide. The results show that inequalities arise from the fractal structure of the socioeconomic network.