Large language models (LLMs) are being deployed at scale in consequential real-world systems, from financial markets to content moderation to hiring. We show that improving individual model capability can degrade rather than improve system-level outcomes. We hypothesize that shared training and architectures can lead more capable LLMs to behave more similarly, creating correlated actions that do not diversify away. We develop a general framework showing how this correlation creates a non-diversifiable risk floor and test its predictions in financial markets using an agent-based simulation with LLM traders of varying general-purpose capability. We find that: (1) frontier LLMs exhibit significantly correlated behavior that increases with capability; (2) when their shared reasoning is accurate, increasing agent participation reduces market-level risk; and (3) when agents share a common misinformation environment, the same correlated behavior becomes a liability. Together, these results identify a capability paradox: improving individual models does not necessarily produce better system-level outcomes. Whether the same dynamics arise in other domains is an open empirical question.

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