Judge Hacking in Recursive Debate Protocols: A Call for Solutions

The debate protocol is a promising solution to the problem of supervising systems that are more capable than their supervisors, known as scalable oversight. It is proposed not only as an inferencetime procedure for adjudicating individual claims, but as a training protocol: the judge's verdict propagates back through the debate as a reward signal used to optimise the debaters. The judge here can be a human or some proxy for human feedback. Under idealised assumptions, debate incentivises truthfulness: the truthful claim is the uniquely optimal one to defend. Real judges, however, make systematic errors. Human judges exhibit predictable cognitive and domain-specific biases, and AI proxies exhibit predictable hallucinations and distributional failures. We argue that when these leaf-level errors are systematic and learnable, a dishonest debater can sometimes win debates while defending a falsehood or attacking truth by strategically steering the debate towards the judge's blind spots. We call this judge hacking. We ground this intuition in a formal game-theoretic model over recursive debate decomposition trees, where judge hacking occurs when the value of a false claim exceeds that of the corresponding true claim, and we speculate that the same mechanism plausibly arises across other variants of debate such as cross-examination and prover-estimator. The risk is most acute when debate is used for training because it introduces strong optimisation pressure to exploit the judge when it is valuable to do so. If debate is to be a viable oversight strategy, judge hacking must be mitigated. We study juries-panels of multiple judges-as a general, judge-side mitigation in need of empirical research. Independent, diverse juries can suppress idiosyncratic errors through a wisdom-of-the-crowd effect, but correlated or homogeneous juries can amplify shared systematic biases. We identify the maximum shared false-positive and false-negative bias over adversarially reachable leaves, together with the correlation structure of juror errors, as the key parameters governing jury robustness. We conclude with a call for urgent empirical and theoretical work on jury design for debate.