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arxiv: 2606.10296 · v1 · pith:TYIDEY22new · submitted 2026-06-09 · 💻 cs.CL · cs.AI

The Confident Liar: Diagnosing Multi-Agent Debate with Log-Probabilities and LLM-as-Judge

Ali Keramati , Justin Cheok , Jacob Horne , Mark Warschauer This is my paper

Pith reviewed 2026-06-27 13:39 UTC · model grok-4.3

classification 💻 cs.CL cs.AI
keywords multi-agent debatelog-probabilitiesLLM-as-judgereasoning qualityconfidence trajectoryrole asymmetrycritical failuresConstructor Auditor
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The pith

In multi-agent debate, a Constructor's token-level confidence predicts externally judged reasoning quality twice as strongly as an Auditor's.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper investigates the links between internal model confidence (token log-probabilities), external LLM-as-judge rubric scores on reasoning quality, and final task accuracy across debate agents. It identifies a consistent four-phase confidence pattern and a clear role asymmetry in the rubric-scoring domain, where confidence tracks judged quality and flags critical failures more reliably for the Constructor than the Auditor. Current debate evaluations focus only on final-answer correctness and therefore miss whether the intermediate reasoning steps are sound. A reader would care because reliable internal signals could let systems monitor and improve the reasoning process itself rather than only the endpoint.

Core claim

Across three domains the work measures how token-level log-probability distributions over reasoning tokens relate to LLM-as-judge scores on instruction following, justification quality, evidence grounding, and a critical-failure flag. In the rubric-scoring domain the data show a four-phase confidence trajectory together with a substantial role asymmetry: confidence correlates with judged reasoning quality roughly twice as strongly for the Constructor as for the Auditor, and confidence-based detection of critical reasoning failures reaches AUROC 0.804 for the Constructor versus 0.634 for the Auditor.

What carries the argument

Two-agent debate architecture pairing a Constructor that generates answers with an Auditor that critiques them, scored by an LLM-as-judge rubric on instruction following, justification quality, evidence grounding, and critical-failure flag, compared against token-level log-probabilities.

If this is right

  • Confidence can serve as a more trustworthy detector of flawed reasoning steps when emitted by the Constructor role.
  • Different monitoring or weighting rules may be needed for each agent because their confidence-quality alignment differs markedly.
  • The observed four-phase confidence trajectory supplies a potential diagnostic signature that future debate runs can check against.
  • Internal confidence and external judge scores may align with final task accuracy in role-specific ways that current end-to-end metrics overlook.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If the asymmetry persists, debate pipelines could route final answers through the higher-confidence Constructor output when the Auditor's signal is weak.
  • Extending the same log-probability versus rubric comparison to the mathematical-reasoning and factual-QA domains could reveal whether the four-phase pattern and role gap are domain-general.
  • Systems might add a lightweight confidence filter that pauses or restarts debate rounds when the Constructor's signal drops below a threshold tied to the observed AUROC.

Load-bearing premise

The LLM-as-judge rubric scores supply an independent and valid external yardstick for reasoning quality that can be compared directly to the model's own token log-probabilities.

What would settle it

Re-running the rubric-scoring experiments and finding that the correlation between Constructor log-probabilities and judge scores is not reliably larger than the Auditor correlation, or that the AUROC gap for critical-failure detection shrinks below statistical significance.

Figures

Figures reproduced from arXiv: 2606.10296 by Ali Keramati, Jacob Horne, Justin Cheok, Mark Warschauer.

Figure 1
Figure 1. Figure 1: Overview of the proposed framework. A multi-agent debate system generates structured reason￾ing over a task input; token-level log-probabilities are extracted alongside each generation; a separate LLM-as￾judge module scores the reasoning; and all three signals are correlated and analyzed. completed debate transcript and produces the final task output yˆ. Formally, for each task instance (x, c, y∗ ), the de… view at source ↗
Figure 2
Figure 2. Figure 2: Mean token-level confidence trajectories for [PITH_FULL_IMAGE:figures/full_fig_p009_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: System instructions for the Constructor agent. The [PITH_FULL_IMAGE:figures/full_fig_p013_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: System instructions for the Auditor agent. [PITH_FULL_IMAGE:figures/full_fig_p013_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: System instructions for the Synthesizer agent. [PITH_FULL_IMAGE:figures/full_fig_p014_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: System instructions for the meta-evaluator agent. [PITH_FULL_IMAGE:figures/full_fig_p015_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Task prompt provided to the meta-evaluator at runtime. [PITH_FULL_IMAGE:figures/full_fig_p015_7.png] view at source ↗
read the original abstract

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.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 0 minor

Summary. The paper examines the relationship between token-level log-probability distributions over reasoning tokens, LLM-as-judge rubric scores (instruction following, justification quality, evidence grounding, critical-failure flag), and final task accuracy in a two-agent debate setup (Constructor and Auditor). It reports a consistent four-phase confidence trajectory in the rubric-scoring domain along with a role asymmetry: log-prob confidence aligns roughly twice as strongly with judged reasoning quality for the Constructor, and confidence-based detection of critical reasoning failures yields AUROC 0.804 for the Constructor versus 0.634 for the Auditor. The work motivates extending the analysis to mathematical reasoning and factual QA domains.

Significance. If the LLM-as-judge rubric scores prove to be a valid independent measure of reasoning quality, the reported asymmetries and four-phase pattern would provide a concrete diagnostic tool for intermediate reasoning in multi-agent debate that goes beyond final-answer accuracy. The explicit pairing of internal confidence signals with external rubric evaluation and the cross-role comparison constitute a clear, falsifiable contribution that could inform the design of more reliable debate protocols.

major comments (2)
  1. [Abstract] Abstract: The reported AUROC values (0.804 vs 0.634) and four-phase trajectory are presented as concrete experimental findings, yet the abstract supplies no description of the models, datasets, prompt templates, statistical tests, or controls used to obtain them. Without these details it is impossible to determine whether the asymmetry is robust or an artifact of post-hoc analysis choices.
  2. [Abstract] Abstract (and implied experimental sections): The central claim that confidence-based detection is markedly more reliable for the Constructor rests on the LLM-as-judge rubric scores constituting an independent external measure of reasoning quality. No human inter-annotator agreement, correlation with downstream task accuracy beyond the final answer, or ablation against surface features already captured by log-probs is mentioned, leaving the 2× alignment difference and AUROC gap vulnerable to judge bias.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive feedback. We address each major comment below and have revised the manuscript to improve transparency while acknowledging the scope of our current validation.

read point-by-point responses

  1. Referee: [Abstract] Abstract: The reported AUROC values (0.804 vs 0.634) and four-phase trajectory are presented as concrete experimental findings, yet the abstract supplies no description of the models, datasets, prompt templates, statistical tests, or controls used to obtain them. Without these details it is impossible to determine whether the asymmetry is robust or an artifact of post-hoc analysis choices.

    Authors: We agree that the abstract should supply sufficient experimental context. The revised abstract now includes a concise description of the models used for debate and judging, the rubric-scoring domain in which the four-phase trajectory and AUROC results were obtained, the cross-domain motivation, and the statistical measures (AUROC for critical-failure detection). These additions allow readers to assess the reported asymmetry without immediate reference to the full text. revision: yes

  2. Referee: [Abstract] Abstract (and implied experimental sections): The central claim that confidence-based detection is markedly more reliable for the Constructor rests on the LLM-as-judge rubric scores constituting an independent external measure of reasoning quality. No human inter-annotator agreement, correlation with downstream task accuracy beyond the final answer, or ablation against surface features already captured by log-probs is mentioned, leaving the 2× alignment difference and AUROC gap vulnerable to judge bias.

    Authors: We acknowledge this limitation. The LLM-as-judge serves as a proxy measure in the present work. In revision we have (1) added explicit reporting of correlations between rubric scores and final task accuracy, (2) inserted a limitations subsection that notes the absence of human inter-annotator agreement and the potential for judge bias, and (3) discussed why the observed role asymmetry is unlikely to arise solely from surface features captured by log-probabilities, given its consistency across domains. A full human validation study and surface-feature ablation lie outside the current scope but are noted as future work. revision: partial

Circularity Check

0 steps flagged

No circularity: purely observational experimental comparisons

full rationale

The paper reports direct experimental measurements of three signals (token log-probabilities, LLM-as-judge rubric scores on four dimensions, and final accuracy) across debate roles without any equations, parameter fitting presented as prediction, self-definitional constructs, or load-bearing self-citations. The four-phase trajectory and Constructor/Auditor asymmetries are stated as observed patterns from the data, not quantities derived from or equivalent to the inputs by construction. The LLM-as-judge rubric is used as an external proxy but is not internally defined in terms of the log-probabilities being compared, satisfying the self-contained criterion.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Only the abstract is available; no explicit free parameters, axioms, or invented entities are stated beyond the implicit assumption that the LLM judge is a valid external evaluator.

axioms (1)
  • domain assumption LLM-as-judge rubric scores constitute a reliable external ground truth for reasoning quality independent of the model's own log-probabilities.
    The entire comparison framework rests on treating judge scores as the reference against which log-probability confidence is measured.

pith-pipeline@v0.9.1-grok · 5750 in / 1354 out tokens · 19195 ms · 2026-06-27T13:39:04.900081+00:00 · methodology

discussion (0)

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