Existence of Hierarchies and Human's Pursuit of Top Hierarchy Lead to Power Law

TL;DR

This paper proposes a hierarchical selection model explaining the universality of power laws across natural and social systems, emphasizing the role of hierarchies and human pursuit of top status.

Contribution

It introduces a new model linking hierarchy structures and power law emergence, supported by analysis of language data and simulations.

Findings

Hierarchies and pursuit of top status lead to power law distributions.

Power law is an emergent property of hierarchical systems.

Universality of hierarchies explains widespread power law phenomena.

Abstract

The power law is ubiquitous in natural and social phenomena, and is considered as a universal relationship between the frequency and its rank for diverse social systems. However, a general model is still lacking to interpret why these seemingly unrelated systems share great similarity. Through a detailed analysis of natural language texts and simulation experiments based on the proposed 'Hierarchical Selection Model', we found that the existence of hierarchies and human's pursuit of top hierarchy lead to the power law. Further, the power law is a statistical and emergent performance of hierarchies, and it is the universality of hierarchies that contributes to the ubiquity of the power law.