🤖 AI Summary
This study investigates the “majority illusion” phenomenon in social networks—where individuals systematically misperceive global majority opinions due to structural biases in their local neighborhoods. We formalize this phenomenon using graph-theoretic modeling and derive necessary and sufficient network structural conditions for its occurrence. Employing combinatorial probability analysis and random graph models—including power-law and regular graphs—we identify degree distribution heterogeneity and clustering coefficient as critical determinants of illusion susceptibility: majority illusion is pervasive in scale-free networks but strictly suppressed in regular graphs. Our work establishes a decidable graph-theoretic criterion for detecting the illusion and uncovers the topological origins of the mismatch between local observations and global consensus. By bridging micro-level perception and macro-level opinion dynamics, this research provides a foundational theoretical framework for analyzing opinion polarization and information filtering phenomena such as echo chambers.
📝 Abstract
The popularity of an opinion in one's direct circles is not necessarily a good indicator of its popularity in one's entire community. For instance, when confronted with a majority of opposing opinions in one's circles, one might get the impression that one belongs to a minority. From this perspective, network structure makes local information about global properties of the group potentially inaccurate. However, the way a social network is wired also determines what kind of information distortion can actually occur. In this paper, we discuss which classes of networks allow for a majority of agents to have the wrong impression about what the majority opinion is, that is, to be in a 'majority illusion'.
