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 $p$.

翻译：多数幻觉是社交网络中的一种现象，指网络整体的多数决策与个人社交圈内的多数决策不一致，导致对大型网络中多数意见的错误认知。本文提出多项式时间算法，通过尽可能少的连接改动即可消除网络中的多数幻觉。此外，我们证明对于大多数p值，确保网络中所有邻域至少达到多数意见的p-比例这一更普遍问题是NP难的。