The Ringelmann Effect in Multi-Agent LLM Systems: A Scaling Law for Effective Team Size

arXiv:2606.02646v1 Announce Type: cross Abstract: Inference-time multi-agent LLM scaling lacks a shared unit: counting nominal agents conflates cost with independent evidence. We derive a two-parameter scaling law R(N) = N_ext{eff}/N = 1/(1+c(N-1)N^{-eta}) where the regime exponent eta classifies any configuration into one of three asymptotic regimes -- hard-ceiling at 1/c (eta = 0), sublinear at N^eta/c (0 0.99; only (c, eta) shifts. On free-form math, dense peer influence collapses the answer-level regime from sublinear into hard-ceiling; correctness-level fits remain hard-ceiling throughout. Three findings have practical implications. (i)~Thirty dense debating agents produce no more answer diversity than one on MMLU-Hard. (ii)~A noise placebo tracks self-correction on free-form math and at 4imes scale, so within homogeneous teams the gain commonly attributed to ``debate'' comes from re-evaluation, not peer content. (iii)~A single N le 5 pilot predicts the N=30 structural ceiling, and within the configurations tested only architectural diversity (heterogeneous teams) lowers c and escapes the hard-ceiling regime, communication-mode interventions do not.

Source: arXiv cs.AI | 2026-06-03