Quantifying and Minimizing Perception Gap in Social Networks

TL;DR

This work introduces the Perception Gap Index to quantify local–global misperception in social networks and generalizes the majority illusion to continuous opinions in $[-1,1]$. It derives spectral bounds linking the gap to eigenvalues of the normalized adjacency matrix, showing that better connectivity reduces distortion while pronounced community structure increases it, with closed-form SBM insights for two polarized blocks. The authors prove that minimizing the gap via edge additions is NP-hard to approximate and not monotone or submodular, yet they offer efficient greedy and batch greedy heuristics along with a novel MPC-based pruning method that enables near-optimal solutions on real and synthetic networks. Experimental results on diverse datasets demonstrate that the proposed heuristics effectively reduce the perception gap, supporting practical interventions to mitigate misperceptions in online platforms. Overall, the paper provides a rigorous framework for understanding and mitigating local–global opinion distortions through graph structure and targeted link recommendations, with implications for designing more accurate information ecosystems.

Abstract

Social media has transformed global communication, yet its network structure can systematically distort perceptions through effects like the majority illusion and echo chambers. We introduce the perception gap index, a graph-based measure that quantifies local-global opinion divergence, which can be viewed as a generalization of the majority illusion to continuous settings. Using techniques from spectral graph theory, we demonstrate that higher connectivity makes networks more resilient to perception distortion. Our analysis of stochastic block models, however, shows that pronounced community structure increases vulnerability. We also study the problem of minimizing the perception gap via link recommendation with a fixed budget. We prove that this problem does not admit a polynomial-time algorithm for any bounded approximation ratio, unless P = NP. However, we propose a collection of efficient heuristic methods that have been demonstrated to produce near-optimal solutions on real-world network data.

Figures (5)

• Figure 1: An example of adding edge to reduce the perception gap.
• Figure 2: Illustration of the reduction from GPP to Problem \ref{['minkpolarization']} for $N=7$ and $k=3$. Red edges denote the subset $T$ of $k$ added edges connecting $u_0$ to selected nodes.
• Figure 3: Examples showing non-monotonicity (left) and non-supermodularity (right) for the objective function of Problem \ref{['minkpolarization']}.
• Figure 4: Value of perception gap by adding different numbers of edges for the studied algorithms on our real-world and synthetic networks (Random's performance is poor also in the second row, and thus is omitted to make the difference between other algorithms more distinct).
• Figure 5: The Greedy algorithm eliminates the perception gap in a graph of $M=100$ cliques (each with two $+1$ and two $-1$ nodes); right: graph evolution as inter-clique edges are added.

Theorems & Definitions (15)

• Definition 1: Perception Gap
• Theorem 1: Perception Gap Bounds
• proof
• Theorem 2
• proof
• Theorem 3
• proof
• Theorem 4
• proof
• Lemma 1