Eliminating Majority Illusion Is Easy

Majority Illusion is a phenomenon in social networks wherein the decision by the majority of the network is not the same as one's personal social circle's majority, leading to an incorrect perception of the majority in a large network. In this paper, we present polynomial-time algorithms which can eliminate majority illusion in a network by altering as few connections as possible. Additionally, we prove that the more general problem of ensuring all neighbourhoods in the network are at least a $p$-fraction of the majority is NP-hard for most values of $p$.