The argument from redundant independent evidence
The argument
Within the prover-estimator framework it is proved that a stable decomposition exists whenever the human-judgeable claims at the base of an argument each have sufficiently many independent pieces of supporting evidence, by a majority-vote construction. Correct answers to real oversight questions typically have such support, since a sound conclusion built on imprecise human judgments does not hang on any single one of them, and a judge can tell that the pieces are independent. The honest debater needs only one stable decomposition and is trained to find it. Therefore real oversight questions admit decompositions stable enough for the guarantees.
Does it work?
- Does it follow?
- likely if the premises holdIf the premises are true, the conclusion is much more likely, though not guaranteed.constitution →
- Do the premises hold?
- 1 supported1 not separately assessed
Granting its premises, the conclusion follows for the questions the premises cover: the existence result is a theorem within the prover-estimator framework, and one stable decomposition is all the honest debater needs. It falls short of certainty because "typically" leaves a remainder, and because existence of a stable argument does not guarantee that a bounded debater can find it. The weight rests on the premise that correct answers to oversight questions typically have many independent supports, which has not been assessed, which the protocol's own authors treat as an open empirical question, and which looks doubtful outside conclusions pooled from many measurements. The companion consideration that fragile arguments deserve suspicion is a reason to reject unstable arguments, not a reason to expect stable ones to exist.
Premises
- UnassessedNo current assessment. Attention goes where its expected value is highest and someone funds it; nothing has funded an assessment of this claim yet, and anyone can.constitution →Correct answers to real-world AI oversight questions are typically supported by many independent pieces of evidence.
- SupportedThe evidence favors the claim, but the examination is incomplete or the evidence is indirect.constitution →Under stability assumptions, prover-estimator debate provably lets an honest debater defeat obfuscated arguments with computational effort comparable to the dishonest debater's.
Where it is made
Passages where sources make, criticize or mention this argument. They record where it appears, not how strong it is, and none has precedence over another.
- Prover-Estimator Debate: A New Scalable Oversight Protocolmakes itstates it fullyThe passage states the inference with what it needs.constitution →
We prove that such stable arguments exist whenever the truth is supported by sufficiently many independent pieces of evidence. If one relies on independence of supporting evidence to produce stable arguments, one must at a minimum have some reason to believe that the pieces of evidence are actually independent. For example, if a human judge is given three pieces of evidence for a claim, can they accurately say whether the truth-values of each piece of evidence are independent?
Jonah Brown-Cohen and Geoffrey Irving · 2025-06-17
- How to Have a Sensitive Debate: An Instance-Optimal Protocol for AI Debatemakes itleaves a premise unstatedThe passage relies on a premise the inference needs without saying it.constitution →
This in turn requires Alice to only decompose her claims in a way that is not too sensitive to errors in individual sub-claims. We view this as a very natural restriction when arguing about claims that inherently involve fuzzy human judgment. Indeed, one should be very suspicious of any argument that is highly sensitive to changes in individual pieces of evidence, and yet relies on fuzzy human judgments in each step.
arXiv · 2026-10