Asymptotics for Pull on the Complete Graph

Consider the following model to study adversarial effects on opinion forming. A set of initially selected experts form their binary opinion while being influenced by an adversary, who may convince some of them of the falsehood. All other participants in the network then take the opinion of the majority of their neighbouring experts. Can the adversary influence the experts in such a way that the majority of the network believes the falsehood? Alon et al. [1] conjectured that in this context an iterative dissemination process will always be beneficial to the adversary. This work provides a counterexample to that conjecture. [1] N. Alon, M. Feldman, O. Lev, and M. Tennenholtz. How Robust Is the Wisdom of the Crowds? In Proceedings of the 24th International Joint Conference on Artificial Intelligence (IJCAI 2015), pages 2055-2061, 2015.