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Fractal Social Dynamics as a Driver of Consensus and Inequality

Airton Deppman

TL;DR

Problem: how consensus formation and inequality arise in stratified social networks. Approach: fractal network modeling with fixed scaling combined with $q$-calculus to derive a generalized Boltzmann framework and the Plastino-Plastino Equation, producing $q$-Gaussian stationary states. Findings: heavy-tailed distributions and superlinear scaling emerge naturally from the fractal structure and transport coefficients, with inequalities driven by hierarchical interactions rather than external drivers. Significance: provides a principled link between micro-level social ties and macro-level urban wealth and information dynamics, with testable predictions and policy-relevant implications.

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.

Fractal Social Dynamics as a Driver of Consensus and Inequality

TL;DR

Problem: how consensus formation and inequality arise in stratified social networks. Approach: fractal network modeling with fixed scaling combined with -calculus to derive a generalized Boltzmann framework and the Plastino-Plastino Equation, producing -Gaussian stationary states. Findings: heavy-tailed distributions and superlinear scaling emerge naturally from the fractal structure and transport coefficients, with inequalities driven by hierarchical interactions rather than external drivers. Significance: provides a principled link between micro-level social ties and macro-level urban wealth and information dynamics, with testable predictions and policy-relevant implications.

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 -calculus, the model reveals how hierarchical structures influence information spread, highlighting universal features governed by power laws.. The results follow -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.

Paper Structure

This paper contains 3 sections, 13 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Theoretical Background
  3. Conclusion

Figures (1)

  • Figure 1: Visual representation of q-Gaussian distributions and their product with a linear function, illustrating the effect of varying $q$ on distribution shapes.