Current training methods reliably bring AI debaters close to the equilibria assumed by debate's theoretical guarantees.

The theoretical guarantees of AI debate (from the original debate proposal through doubly-efficient and prover-estimator debate) are statements about what holds at an equilibrium, or approximate equilibrium, of the debate game. Whether practical training brings debaters there is a separate empirical question, and the evidence does not show that it does.

Gradient-based self-play has no general convergence guarantee in two-player games, and nearness to equilibrium is hard to certify: a debater that withholds a winning line of argument during training ("exploration hacking") is indistinguishable from one that lacks it. The authors of the UK AI Security Institute's debate safety-case sketch (2025) identify exploration guarantees, which the sketch needs in order to argue that training reached approximate global equilibrium, as a major gap about which "we know very little." Published debate-training experiments (for example self-play and persuasiveness-optimised debaters on reading-comprehension tasks in 2024) are short, use shallow protocols on closed-ended questions, and report improved judge accuracy in some settings, but none measures distance from equilibrium or shows it reliably small on open-ended tasks.

The claim is therefore doubtful rather than contradicted: there is no positive demonstration that training fails to approach equilibrium either, and the matter is chiefly one of absent evidence where a field actively seeking it has not found it. A method for certifying near-equilibrium play, or experiments showing trained debaters cannot be beaten by targeted best-response search, would change this verdict.