The Impact of Random Actions on Opinion Dynamics

Opinion dynamics have fascinated researchers for centuries. The ability of societies to learn as well as the emergence of irrational herding are equally evident. The simplest example is that of agents that have to determine a binary action, under peer pressure coming from the decisions observed. By modifying several popular models for opinion dynamics so that agents internalize random actions rather than smooth estimates of what other people think, we are able to prove that almost surely the actions final outcome remains random, even though actions can be consensual or polarized depending on the model. This is a theoretical confirmation that the mechanism that leads to the emergence of irrational herding behavior lies in the loss of nuanced information regarding the privately held beliefs behind the individuals decisions. Interestingly, in expectation, all these models correspond to classical opinion dynamics models. This means that in every event the temporal evolution of the society does not follow the mean behavior predicted by classical models. We also provide a simple argument that shows that the final descent into the herd is exponential and does not depend on the network topology.