Information cascade final size distributions derived from urn models

Abstract

Bipolarization is a phenomenon in which either a large or very small information cascade appears randomly when the retweet rate is high. This phenomenon, which has been observed only in simulations, has the potential to significantly advance the prediction of final cascade sizes because forecasters need only focus on the two peaks in the final cascade size distribution rather than considering the effects of various details, such as network structure and user behavioral patterns. The phenomenon also suggests the difficulty of identifying factors that lead to the emergence of large-scale cascades. To verify the existence of bipolarization, this paper theoretically derives mathematical expressions of the cascade final size distribution using urn models, which simplify the diffusion behavior of actual online social networks. Under the assumption of infinite network size, the distribution exhibits power-law behavior, consistent with the results of existing diffusion models and previous Twitter analytical outcomes. Under the assumption of finite network size, bipolarization is observed.