two-heads-are-better-than-one

Two heads are better than one

“Two people working on a problem will do better than either alone.”

Origin

English proverb, recorded from the sixteenth century (John Heywood, 1546). About people pooling independent knowledge and catching each other's errors.

Why it should, or should not, apply to models

The benefit with people comes from independence: two heads hold different facts and different mistakes. Two instances of the same model, given the same context, hold the same facts and the same mistakes, so the proverb should transfer only to the extent the heads are actually different — in model, in context, or in the evidence each holds. It predicts that sharing everything between agents removes the benefit and can make things worse, because a shared error is then reinforced rather than caught.

Standing: Untested

From reviewed claims only. Unreviewed claims are listed below and marked, and move nothing.

Where it breaks

Claims showing the adage failing for models.

In multi-agent LLM systems where one agent starts with an erroneous shared belief, broadcasting every agent's full context at every step raises the rate of false assertions above doing no synchronization at all, because the error propagates to agents that were previously correct — and the harm appears only in tasks where one wrong fact cascades across semantically linked dimensions (destination to airport to weather), not where agent contexts are largely orthogonal.
Stating false facts confidentlypending review
Broadcasting every agent's full context raised the rate of false assertions above no synchronisation at all: one wrong head corrupted the others. The proverb's premise, independent heads, was absent.

Where it holds only under a condition

Claims that keep the adage but bound it.

The agent that produced an artifact is a biased judge of it — it holds the context and the incentives that skew its assessment — so verification belongs with a deterministic sensor or a separate verifier that reports failures back rather than rewriting the output, and in a multi-agent system the verifier is the one component no agent may override.
Fixing its own mistakespending review
A second agent helps as a verifier when it does not share the producer's context. The condition is independence, not headcount.

Add a case where it holds or breaks

A break is worth more than a hold. If you have seen this fail for a model, with the setup written down, that is the most useful thing you can add here.

Notes

Wanted: a measured case where a second agent with independent context raised accuracy over a single agent on the same task, to pair with the break above. Debate and ensemble papers are the place to look.