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.
How can common ground between societies in conflict be identified when citizens' acceptability of peace agreements is shaped by contested narratives? Such acceptability is mediated not only by the clauses that agreements include or exclude, but crucially by citizens' subjective reasoning concerning agreements' clauses. In this paper, we leverage computational argumentation to introduce a novel approach to identifying mutually acceptable agreements among individuals in conflict, i.e. a Zone of Possible Agreement (ZOPA). First, we introduce a quantitative bipolar argumentation framework tailored to represent each side's reasoning about peace agreements. We then show how merging these frameworks can enable negotiators to identify peace agreements that are mutually acceptable. To evaluate our approach under conditions of real-world relevance, we focus on the Palestinian-Israeli conflict, where long-standing policy, practitioner and public interest underscores the demand for methods capable of analysing polarised public reasoning. We show how our framework identifies a ZOPA through theoretical analysis and preliminary experiments using survey data from both existing work and retrieved by a large language model. The results illustrate how argumentation can empower negotiators and conflict-resolution teams in mapping feasible ZOPAs grounded in citizens' reasoning.