Dynamic influence networks self-organize towards non-normal socio-economic instabilities

Large-scale synchronization in socio-economic systems is often modeled through Ising-like dynamics, where critical transitions mark the onset of collective alignment. Yet, even away from these critical points, instabilities can still arise when the underlying interaction network is strongly non-normal, that is, when influence is asymmetric and hierarchical. In such networks, shocks may be transiently amplified despite the system being globally stable, creating the appearance of synchronization and collective shifts without requiring proximity to a critical threshold. While this insight has expanded our understanding of endogenous instabilities, most existing models treat the influence network as fixed and exogenous, leaving open the question of how such non-normal structures might emerge from agent behavior. By studying financial markets as a prime example of a socio-economic system, we address this gap by showing that feedback between individual trader dynamics and market outcomes causes the influence network to evolve toward increasingly non-normal configurations. This process, which we term self-organized non-normality, drives the system into a sensitive, instability-prone state without requiring fine-tuning. Using agent-based simulations and data from the eToro trading platform, we show that traders adapt their social ties based on observed performance and popularity, producing increasingly centralized influence networks. This reinforces market trends and amplifies volatility, creating a feedback loop between behavior and influence structure that helps explain the spontaneous emergence of socio-economic instabilities such as financial bubbles, opinion cascades or collective polarization.