Let the debate stop itself
The first version of multi-agent's arena ran a fixed number of rounds. Three models, four rounds, every time. Half of those rounds were theater. By round two nobody was changing position, they were just saying the same thing with more tokens.
Now the rounds are convergence gated. You set a minimum and a maximum, and the arena adds another round only while positions keep moving: someone withdraws a claim, adopts a rival's finding, or raises a new one. The moment the debate freezes, it ends and the judge takes over.
Fixed iteration counts are a smell in any adversarial process. If nothing changed in the last round, the next one is a waste of tokens. Measure movement, not laps.