When can weak models match strong model performance?

Can a committee of weak reasoning-model calls reach the performance of a much stronger model? The honest answer is "yes, but not because more agents help." The mechanism is boosting: sampling exposes latent correct solutions in the proposal pool, but critics and comparators must then recover them without access to the hidden verifier.

The paper separates four quantities — proposal coverage, local identifiability, progress, and diversity — and proves a sharp limit. Repeated sampling can amplify coverage, but coverage alone cannot create useful critics or comparators. Reliable amplification requires an additional local soundness signal: execution, proof checking, type checking, tests, or constraint solving. With it, rank-based bounds show when local selection errors compose into reliable trajectories. Without it, weak-model failure is revealed as a selection failure, not an information failure — on SWE-bench Verified, hidden-test-passing patches often appear in a pool of nano-model proposals even when a single call fails.

This identifies two distinct ceilings. When a correct patch is in the pool but the harness picks another, the bottleneck is identifiability — better critics, tests, or aggregation help. When no correct patch appears at all, the bottleneck is coverage — no selector can recover an absent solution. The result disciplines the "scale up agents" intuition: it pins the gain to verifiable domains and to the presence of a sound local check. It extends What limits how much models can improve themselves? to the committee setting — the verification advantage is what turns latent coverage into solve rate.