Current models for opinion dynamics typically utilize a Poisson process for speaker selection, making the waiting time between events exponentially distributed. Human interaction tends to be a more bursty process, though, having higher probabilities of either extremely short waiting times or long periods of silence rather than the relative regularity of Poisson selection. To quantify the effects this difference may have on the dynamics of social models, we place in competition two groups exhibiting different speakers waiting-time distributions. These competitions are implemented in the binary Naming Game and in the voter model, showing that the relevant aspect of the waiting-time distribution is the density of the head rather than that of the tail. In fact, we show that even with identical mean waiting times, a group with a higher density of short waiting times is favored in competition over the group with a less bursty distribution. This effect remains in the presence of nodes holding a single opinion that never changes, as the fraction of such committed individuals necessary for achieving consensus decreases dramatically when their waiting-time distribution has a higher head density than the waiting-time distribution of the nodes holding competing opinions.
['Casey Doyle', 'Boleslaw K. Szymanski', 'Gyorgy Korniss']
The Effects of Communication Burstiness on Consensus Formation and Tipping Points in Social Dynamics