Robust dynamic classes revealed by measuring the response function of a social system

TL;DR

This study analyzes YouTube view dynamics, revealing that while most activity follows a Poisson process, many exhibit power-law relaxation with three distinct classes, modeled by an epidemic process on social networks.

Contribution

It introduces a classification of social system responses into three classes based on relaxation exponents and extends the fluctuation-dissipation theorem concept to social dynamics.

Findings

Most activity is Poissonian.

Existence of three distinct relaxation classes.

Power-law relaxation governs a significant portion of activity.

Abstract

We study the relaxation response of a social system after endogenous and exogenous bursts of activity using the time-series of daily views for nearly 5 million videos on YouTube. We find that most activity can be described accurately as a Poisson process. However, we also find hundreds of thousands of examples in which a burst of activity is followed by an ubiquitous power-law relaxation governing the timing of views. We find that these relaxation exponents cluster into three distinct classes, and allow for the classification of collective human dynamics. This is consistent with an epidemic model on a social network containing two ingredients: A power law distribution of waiting times between cause and action and an epidemic cascade of actions becoming the cause of future actions. This model is a conceptual extension of the fluctuation-dissipation theorem to social systems, and provides a unique framework for the investigation of timing in complex systems.