Debates have recently emerged as a useful methodology for agentic AI to improve performance as well as to aid explainability and user engagement. For example, LLM-empowered agents may debate internally (with themselves) and/or externally (with other agents). In many settings where debates are used, debates' outcomes and resulting outputs are determined post-hoc by external judges, often LLMs. In this paper we develop and test a novel theory of debate judgement applicable to all settings where agents engage in debates by providing pros and cons for their opinions therein. Specifically, we identify a number of formal properties that debate judgement may be required to satisfy in general, as concerns reproducibility, robustness, groundedness and explainability. Then, we explore their satisfaction formally and/or experimentally, for claim verification settings, for two specific alternative debate judgement methods: variants of the LLMs as a judge idea and formal semantics drawn from computational argumentation. We show that the two methods give similar accuracy performances but the former may lack formal guarantees that the latter brings. Overall, our study indicates argumentation semantics as an ideal candidate for principled judges in debate-driven AI.
AI agents can draft claims faster than authors can check whether the cited or retrieved evidence supports them. We study evidence-ledger adjudication: a claim-evidence traceability workflow that pairs each claim with an evidence packet, assigns a support relation, and routes unsupported, contradicted, or mixed-evidence claims back to the author. The empirical core is a 2,335-row blind benchmark built from independent external labels in AVeriTeC, CLIMATE-FEVER, and SciFact. Gold relations and source evidence labels are hidden during prediction and joined only for scoring. On this benchmark, the agent evidence-ledger condition achieves 0.676 relation accuracy and 0.601 macro-F1, compared with 0.383 accuracy and 0.303 macro-F1 for the best non-agent baseline. It also routes 1270/1435 claims whose gold labels indicate contradiction, missing evidence, or mixed evidence, while routing 295/900 supported claims. These results show that evidence-ledger adjudication can turn heterogeneous evidence packets into an auditable traceability layer for AI-assisted writing.