A Theory of Post-hoc Debate Judgement

Multi-agent debate systems are typically evaluated only on whether the final answer is correct, overlooking the quality of the intermediate reasoning that debate is designed to produce. This paper studies the relationship between three signals in multi-agent debate: token-level log-probability distributions over reasoning tokens, LLM-as-judge rubric scores assigned to those tokens, and final task accuracy. We examine whether internal confidence signals predict externally evaluated reasoning quality, and whether either signal aligns with task correctness, across three domains: rubric-based scoring, mathematical reasoning, and factual question answering. Our framework pairs a two-agent debate architecture -- a Constructor and an Auditor -- with an LLM-as-judge that scores each agent's reasoning along instruction following, justification quality, and evidence grounding, together with a critical-failure flag. Experiments in the rubric-scoring domain reveal a consistent four-phase confidence trajectory and a substantial role asymmetry: confidence aligns with judged reasoning quality roughly twice as strongly for the Constructor as for the Auditor, and confidence-based detection of critical reasoning failures is markedly more reliable for the Constructor (AUROC 0.804) than for the Auditor (0.634). These findings motivate the broader cross-domain investigation proposed in this paper.

Multi-agent debate, in which several LLMs exchange arguments before producing an answer, raises a basic question: does expressed disagreement reflect changes in the members' own positions? No single signal can settle this question, so we organize the analysis around five questions: (A) does the debater say it disagrees; (B) does its reply text actually argue; (C) does its own position change after each debate turn; (D) how much, quantitatively, does the position change; and (E) how do members' final positions compare with their initial ones? We evaluate two- and three-member committees on 50 curated opinion questions from GlobalOpinionQA, using same-model, same-family, and mixed-family configurations with friendly, neutral, and hostile instructions assigned at each turn. (A) Tone changes reported agreement: the share of replies reporting strong agreement is 70.7-96.3% under friendly instructions, compared with 9.5-19.3% under hostile ones, varying with model choice. (B) Self-reports broadly align with text judgments, but consistency varies by agreement level and model choice. (C) Position changes depend on the interaction: after a peer's leaning-disagree reply, members reporting strong agreement switch options more often than those reporting leaning disagreement. (D) For open-weight members, the probability of the option a member already holds stays near saturation, even after a peer's pushback, while endorsement of its earlier position text drops after a peer's argument relative to neutral filler, more for Qwen3.8-27B than Inkling. (E) The selected option is unchanged from members' initial to final positions in over 90% of comparisons in every configuration. Taken together, expressed disagreement need not translate into position revision, either within individual exchanges or over a complete debate.

Multi-agent debate has emerged as a promising approach for improving LLM reasoning on ground-truth tasks, yet current methodologies face certain structural limitations: debate tends to induce a martingale over belief trajectories, majority voting accounts for most observed gains, and LLMs exhibit confidence escalation rather than calibration across rounds. We argue that the genuine value of debate, and dialectic systems as a whole, lies not in ground-truth tasks but in defeasible domains, where every position can in principle be defeated by better reasoning. We present the Council of Hierarchical Agentic Language (CHAL), a multi-agent dialectic framework that treats defeasible argumentation as an engine for belief optimization. Each agent maintains a CHAL Belief Schema (CBS), a graph-structured belief representation with a Bayesian-inspired architecture, that facilitates belief revision through a gradient-informed dynamic mechanism by leveraging the strength of the belief's thesis as a differentiable objective. Meta-cognitive value systems spanning epistemology, logic, and ethics are elevated to configurable hyperparameters governing agent reasoning and adjudication outcomes. We provide a series of ablation experiments that demonstrate systematic and interpretable effects: the adjudicator's value system determines the debate's overall trajectories in latent belief space, council diversity refines beliefs for all participants, and the framework generalizes across broad fields. CHAL is, to our knowledge, the first framework to treat multi-agent debate as structured belief optimization over defeasible domains. Further, the auditable belief artifacts it produces establish the foundation for dedicated evaluation suites for defeasible argumentation, with broader implications for building AI systems whose reasoning and value commitments are transparent, aligned, and subject to human oversight.