Infinitesimal Interference Has Substantial Impact: Quantifying the Influence of Minimal Bot Presence on Consensus Formation in Social Networks

Abstract

We study the impact of bots on social learning in a social network setting. We show that the consensus of the network expressed as a mapping of the interaction rate between the agents and bots is discontinuous at zero mass of bots. This implies that even a comparatively “infinitesimal” small number of bots still has a sizeable impact on the consensus and hence represents an obstruction to the “wisdom of crowds”. Morevoer, we prove that the consensus gap induced by the marginal presence of bots depends neither on the agent network or bot layout nor on the assumed connection structure between agents and bots. Fortunately, before the ultimate (and bot-infected) consensus is reached, the network passes through a quasi-stationary phase which offers the potential to mitigate the harmful impact of bots.

Keywords: Learning, misinformation, social networks, social media, wisdom of crowds, fake news