Researchers have proposed a new theory of post-hoc debate judgement for artificial intelligence systems. Debates are used to improve performance and explainability in AI, but their outcomes are often determined by external judges. The authors identify formal properties that debate judgement should satisfy, such as reproducibility and robustness. They test two alternative methods: using large language models as judges or formal semantics from computational argumentation. The study suggests that the latter method is more suitable for principled judges in AI debates. --- Why it matters: This research matters to engineers and researchers in AI because it addresses a critical challenge in debate-driven AI systems: ensuring the fairness and reliability of post-hoc judgement. By developing a theory of debate judgement, the authors provide a framework for designing more robust and explainable AI systems. Source: https://arxiv.org/abs/2608.19002