Opinion Dynamics in the Presence of Bots

We propose a variant of the voter model which captures salient features of opinion dynamics in a network consisting of individuals and bots. Key features of our model are that the influence of bots on the opinion evolution can be different from the influence of individuals in the network and that the opinion of bots does not evolve over time irrespective of the opinion of the rest of the network. We use the proposed model and tools from the theory of stochastic approximation and martingales to develop a method to accurately characterize the number of bots needed to achieve specific opinion-shaping targets as a function of various system parameters in a fully connected network.