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Attributing Emergence in Million-Agent Systems

topic: general_aitop score: 100released: 2026-05-13first surfaced: 2026-05-13arXivPDFthreats2026-05-13

Authors: Ling Tang, Jilin Mei, Qian Chen et al.

arXiv · PDF

Summary

The authors develop a fast method to figure out which individual agents in a million-user LLM-powered social simulation are responsible for macro-scale behaviors like polarization or information cascades. Traditional attribution methods (like Shapley values) scale combinatorially and max out around a thousand agents, but social phenomena happen at millions. They adapt a path-integral approach that runs 10,000–100,000× faster and use it on real Bluesky data (1.6M users). They find that small-sample studies (N=100) massively overattribute influence to high-follower accounts, while full-scale analysis reveals the long tail and middle tier jointly carry most of the weight — and they prove mathematically that you can't fix this by rescaling.

Main takeaways:

  • Existing attribution methods for multi-agent systems can't scale past about 1,000 agents, but the social phenomena we care about (polarization, cascades) happen at millions of users.
  • The new method satisfies all four Shapley axioms but runs four to five orders of magnitude faster, making million-agent attribution feasible.
  • On 1.6M Bluesky users, full-scale attribution disagrees structurally with the small (N=100) convenience samples used in prior work: small samples over-credit high-follower accounts while missing the long tail.
  • The "Attribution Scaling Bias" theorem proves you can't reconcile small-scale and full-scale results with any global rescaling factor when your macro indicator is nonlinear.
  • For any nonlinear emergent behavior, full-scale attribution is a theoretical requirement, not just a nice-to-have.

Relevance

Not directly related to my persona/midtraining work — this is about attributing emergent behavior in multi-agent social simulations, not about how personas are installed or conditioned in single models. Included because it's a rigorous scaling result for emergent phenomena, which might be conceptually useful if I ever think about emergent misalignment or multi-model systems.

Threat model

Potential threat/caveat for clean result "Stretching turn count, completion length, or system-prompt length at train time fails to amplify marker uptake; the longest system prompt instead leaks across bystander personas (LOW confidence)": this item discusses bias.

Abstract

arXiv:2605.11404v1 Announce Type: new Abstract: Large language models (LLMs) can simulate human-like reasoning and decision-making in individual agents. LLM-powered multi-agent systems (MAS) combine such agents to simulate population-scale social phenomena such as polarization, information cascades, and market panics. Such studies require attributing macro emergence to individual agents, but existing axiomatic methods scale combinatorially in $N$ and have been confined to $N \lesssim 10^3$, while the phenomena they explain occur at $N \geq 10^6$. We address this gap by adapting Aumann--Shapley path-integral attribution to LLM-powered MAS at million-agent scale; the resulting method satisfies all four axioms, runs four to five orders of magnitude faster than sampled Shapley on the same hardware. We use this method to test the scale gap empirically: across 14 days of public Bluesky data ($1{,}671{,}587$ active users), we compute the attribution at both full scale and the visibility-biased $N = 10^2$ convenience sample used by small-scale studies, and the two disagree structurally. At full scale the long tail and middle tier jointly carry the majority; the biased small panel attributes almost everything to a few high-follower accounts. We then prove that under any nonlinear macro indicator the disagreement cannot be reduced by post-hoc rescaling: an Attribution Scaling Bias theorem shows that no global rescaling factor can reconcile small-scale and full-scale attribution. Full-scale attribution is therefore not a methodological choice but a theoretical requirement for any nonlinear macro indicator.