What Makes Majority Illusion Easy to Detect?

2026-06-02

AI Summary

This study investigates the "majority illusion" in social networks, wherein individuals mistakenly perceive a minority opinion as dominant, thereby distorting collective decision-making. Given a network structure, the problem asks whether there exists a binary labeling of nodes such that at least a fraction \( q \) of nodes observe a majority of their neighbors holding the globally minority label. Employing computational complexity theory, graph theory, and parameterized algorithms, this work provides the first systematic characterization of the problem’s complexity across various graph classes. It establishes a complete complexity landscape, precisely delineating conditions under which the problem is polynomial-time solvable versus NP-hard, and reveals fundamental connections between structural graph properties and computational tractability.

Abstract

Majority illusion is an undesirable phenomenon in social networks in which agents incorrectly perceive a minority opinion as dominant. This can severely distort collective behavior and decision-making. We study the fundamental question of detecting whether a social network allows for a majority illusion. Formally, in the $q$-Majority Illusion problem, we ask whether there exists a binary labeling of agents in which at least a $q$-fraction of agents have the majority of neighbors with the minority label. We investigate how various structural properties of the underlying social network influence the tractability of this question, and provide a detailed map of its computational complexity.

Problem

• majority illusion
• social networks
• computational complexity
• binary labeling
• collective behavior

Innovation

• majority illusion
• computational complexity
• social networks
• binary labeling
• q-Majority Illusion