Self-Reinforcing Cascades: A Spreading Model for Beliefs or Products of Varying Intensity or Quality

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 nonuniversal 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.