Complexity in Individual Trajectories toward Online Extremism

Figure 2

Memory effects for shorter lifetimes. (a) Plot of conditional expansion terms given a specific event-time lifetime for individuals who will eventually get banned (i.e., future-ban individuals). is the probability that any given individual in our study (i.e., out of all individuals) will get banned and that he/she joins exactly future-ban () groups prior to this banning, conditioned on his/her event-time lifetime until banning being . By definition, and hence are undefined for individuals whose accounts do not get banned. Scattered points: empirical values obtained from the set of individual pathways in our dataset. Solid lines: our finite memory model with parameter value shown and obtained from a maximum likelihood estimate (MLE). Dotted lines: result for a memoryless null model in which individuals have the same average group-joining rate as the data (obtained using MLE), hence yielding a binomial distribution. The largest memory effects arise for the shortest event-time lifetimes. (b) Comparison of the clock-time lifetime distribution from the empirical data (red dots), our mathematical model with memory effects (blue), and without memory effects (green). Error bands are obtained from simulations of the model. is undefined for individuals whose accounts do not get banned. The largest memory effect arises for the shortest clock-time lifetimes.

(a)

(b)