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.