Beyond Individual Influence: The Role of Echo Chambers and Community Seeding in the Multilayer three state q-Voter Model

TL;DR

This paper analyzes influence maximization in a 3-state multilayer q-voter model with LOCAL & AND updates, revealing that in highly modular networks, strategies targeting dense communities (CIM, k-Shell) can trap diffusion due to the Overkill Effect, while sparse, diverse seeding (VoteRank) more effectively triggers global cascades. Through mean-field analysis and extensive mABCD-based simulations on duplex networks, the study identifies a Fortress Trap where local clustering fails, and a Redundancy Trap where perfectly aligned layers impede diffusion. The findings show that diffusion under complex contagion benefits from topological entropy and cross-layer diversity rather than local reinforcement, with VoteRank outperforming structure-based methods across scenarios and noise regimes. The work provides insights into how topological alignment shapes diffusion dynamics and suggests directions for heterogeneous thresholds, real-world multiplex validation, competitive influence scenarios, and temporal network extensions. Overall, this work shifts the strategy in complex contagion from clustering to diversity of reach to overcome multilayer inertia in fragmented digital landscapes.

Abstract

The diffusion of complex opinions is severely hindered in multilayer social networks by echo chambers and cognitive consistency mechanisms. We investigate Influence Maximization strategies within the 3-state multilayer q-voter model. Utilizing the mABCD benchmark, we simulate social environments ranging from integrated Open Worlds to segregated Fortress Worlds. Our results reveal a topological paradox that we term the "Fortress Trap". In highly modular networks, strategies maximizing local density such as Clique Influence Maximization (CIM) and k-Shell fail to trigger global cascades, creating isolated bunkers of consensus due to the Overkill Effect. Furthermore, we identify a Redundancy Trap in perfectly aligned Clan topologies, where the structural overlap of layers creates a "Perfect Prison," rendering it the most resistant environment to diffusion. We demonstrate that VoteRank, a strategy that prioritizes diversity of reach over local intensity, consistently outperforms structure-based methods. These findings suggest that, for complex contagion, maximizing topological entropy is more effective than reinforcing local clusters.

Figures (8)

• Figure 1: Transitions for an Undecided agent ($U$). Conformity with probability $1-p$ (requiring a $q$-sized unanimous panel across all $L$ layers). Spontaneous transitions driven by independence (noise with probability $p$).
• Figure 2: Transitions for a Decided agent ($A$ or $B$).
• Figure 3: Mean Field Approximation results for $q=2$ vs. $q=4$ ($L=2$). The $q=2$ case allows for a wider range of stability with gradual degradation, while $q=4$ maintains higher consensus quality but collapses at a lower noise threshold.
• Figure 4: Deterministic phase-space trajectories for the multilayer $q$-voter model ($q=4, L=2$). Orange dots indicate starting configurations, and red stars indicate final stationary states. Left: For low noise ($p=0.07$), multiple attractors exist depending on initial conditions. Right: For high noise ($p=0.15$), all trajectories collapse into the central Noise Equilibrium.
• Figure 5: Phase transition diagrams ($q=4$).