Self-reinforcing cascades: A spreading model for beliefs or products of varying intensity or quality

TL;DR

This paper introduces a new model for social contagions that incorporates self-reinforcement, showing that such mechanisms lead to power-law cascade sizes over a broad parameter range, unlike traditional models requiring fine tuning.

Contribution

It develops a recursive, dynamic modeling framework for self-reinforcing cascades, revealing a critical regime with universal power-law distributions across diverse parameters.

Findings

Power-law cascade size distributions with non-universal exponents

Self-reinforced cascades exhibit critical-like behavior over wide parameter ranges

Contrasts with classic models requiring fine-tuned critical points

Abstract

Models of how things spread often assume that transmission mechanisms are fixed over time. However, social contagions--the spread of ideas, beliefs, innovations--can lose or gain in momentum as they spread: ideas can get reinforced, beliefs strengthened, products refined. We study the impacts of such self-reinforcement mechanisms in cascade dynamics. We use different mathematical modeling techniques to capture the recursive, yet changing nature of the process. We find a critical regime with a range of power-law cascade size distributions with non-universal scaling exponents. This regime clashes with classic models, where criticality requires fine tuning at a precise critical point. Self-reinforced cascades produce critical-like behavior over a wide range of parameters, which may help explain the ubiquity of power-law distributions in empirical social data.