REVIEW 5 major objections 6 minor 47 references
When Two LLMs Debate, Both Think They'll Win
T0 review · 5 major / 6 minor · reviewed 2026-08-07 · deepseek-v4-flash
Pith's one-line read Large language models cannot reliably assess or update their own confidence in adversarial debate, and become more overconfident as opposition mounts.
desk verdict A useful multi-turn debate testbed for LLM confidence, but the 0-100 'bet' is a strategic stake rather than a clean probability, so the headline 'metacognitive deficit' claim does not follow from the data. read the letter →
The pith
A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.
The reading
What carries the argument
The operative mechanism is the zero-sum debate with private confidence bets. Because exactly one debater can win, two calibrated models cannot both report win probabilities above 50%; mutual high confidence is therefore direct evidence of systematic overconfidence that does not depend on knowing the debate's ground truth. The design combines this zero-sum constraint with a multi-turn format (opening, rebuttal, final) so that belief revision can be tracked as new opposing evidence arrives. The same framework supplies the ablations that isolate the effect: self-debates against identical copies remove opponent differences, an informed condition anchors the true win probability at 50%, and public bets reveal divergence between private reasoning and expressed confidence.
What would settle it
Run the identical three-round debates but pay each model a fixed, non-contingent amount regardless of the bet placed, or instruct it that the bet only measures belief and has no payoff effect. If confidence escalation and mutual high confidence disappear under those conditions, the observed pattern is a payoff artifact; if they persist, the metacognitive deficit reading is supported. A second check is to score calibration against actual win rates determined by a pre-registered neutral judge rather than the models' own beliefs.
Extended reading notes
Core claim
The paper's central claim is that current LLMs exhibit a fundamental metacognitive deficit in dynamic, adversarial settings: they are systematically overconfident at the outset, escalate their confidence when confronted with counter-arguments, and fail to exploit information that logically constrains their win probability. The evidence comes from three-round policy debates in which each model privately placed a 0-100 confidence bet and wrote private reasoning after each speech. Across four experimental configurations, confidence rose from opening to closing rounds in every condition, including a condition where models were explicitly told their odds were exactly 50%; their confidence still drifted from 50.0% to 57.1%. The authors also report that private scratchpad reasoning sometimes contradicts the public bet, with models explicitly saying they bet strategically rather than expressing their true confidence. In their interpretation, verbalized reasoning is often post-hoc justification rather than transparent computation, which challenges chain-of-thought-based interpretability.
Load-bearing premise
The central assumption is that a model's 0-100 'bet' expresses its true subjective chance of winning; if the number is instead a strategic stake chosen to maximize payoff, the escalation and mutual overconfidence findings lose their straightforward meaning.
Editorial extensions
If this is right
- Users of LLM assistants may receive confidently stated but wrong analysis, since models do not reduce confidence when their claims are challenged.
- Agentic systems that rely on numeric confidence signals, such as coding agents, may double down on failing solution paths instead of revising them.
- Explicitly telling a model its win probability is 50% only anchors initial confidence; escalation persists, so calibration cannot be achieved by instruction alone.
- Chain-of-thought monitoring is weakened, because private reasoning traces can diverge from the expressed confidence and may be strategic rather than faithful.
- Simple red-teaming prompts that ask a model to argue the opponent's case reduce escalation, pointing to a cheap partial mitigation.
Reading between the lines
- If the confidence bet is read as a betting stake rather than a subjective probability, the headline escalation numbers may overstate metacognitive failure; a flat-payoff replication would separate strategic betting from genuine belief.
- The same zero-sum design could be ported to other dyadic tasks, such as code repair versus bug reports or medical differential diagnosis versus second opinions, to test whether escalation is a general property or specific to persuasion-style debates.
- The finding that explicit 50% anchoring resets initial confidence but not the drift suggests the drift may be driven by the generation process itself, such as recency of one's own arguments, rather than by evidence evaluation.
- The paper's observation of opposition bias in AI judging hints that evaluation of debate quality is itself unreliable, so confidence calibration may need to be measured against outcome distributions that are independent of any judge.
Editorial analysis
A structured set of objections, weighed in public.
Referee Report
Summary. The paper reports an empirical study in which 10 LLMs debate in 60 three-round policy debates under four conditions (cross-model, self, informed-50%, public bets). After each speech the models privately provide a 0-100 'confidence bet' plus private reasoning. The authors report five findings: high opening confidence (72.92%), escalating confidence across rounds (to 83.26% in cross-model), mutual high confidence (61.7% of cross-model debates with both sides at or above 75%), persistent escalation in self-debates even under an explicit 50% anchor, and frequent divergence between private reasoning and public bets. They conclude that LLMs have a 'fundamental metacognitive deficit' and exhibit 'anti-Bayesian' confidence escalation, with implications for assistant and agentic deployment.
Significance. If the headline claim were supported, the study would be an important contribution to LLM calibration and AI safety, because it would demonstrate systematic overconfidence in dynamic adversarial settings rather than in static QA. The paper has several strengths: it releases code and experimental data, uses four ablation conditions, reports per-model statistics with t-tests, Wilcoxon checks, and standard deviations, and it isolates an interesting phenomenon of escalating stake-setting in LLM debates. The self-debate and informed-50% ablations are thoughtful controls. However, the central inference, that the elicited bets are subjective win probabilities, is invalidated by the paper's own payoff structure, so the quantitative findings do not currently establish a metacognitive deficit. The residual informed-self result is suggestive but uses the same flawed instrument.
major comments (5)
- [§3.4, §4.2–4.3, Appendix N.1.1] The 0–100 elicitation is a payoff-incentivized bet, not a probability elicitation. Appendix N.1.1 gives the payoff rule: a winning debater receives the sum of both bets; a losing debater forfeits his own bet. Under this rule a risk-neutral debater with subjective win probability p>0.5 maximizes expected payoff by betting the maximum, and a debater who expects the opponent to bet high has a strategic reason to bet high regardless of belief. The paper nonetheless labels these numbers 'win probability' in the Abstract and in Tables 1 and 2. Appendix P documents exactly this behavior ('they will certainly bet a high amount too so I should bet the maximum amount to get the max dividend'; 'I'm going to risk a bit more than 50 in order to show how confident I am'). Consequently the headline values (72.9% opening, 83.3% closing, 61.7% mutual high confidence) are uninterpretable as self-assessed win probabilities, and Findings 1–3 as stated are not supported by the data.
- [§4.3, Table 12] The 'logical impossibility' framing requires that both numbers be probabilities of the same binary event. Since the instrument is a stake in a winner-take-all bet, two debaters can both rationally place high stakes even when their subjective probabilities are perfectly coherent (e.g., each believes his own chance exceeds 0.5 and expects the opponent to stake high). The 61.7% 'both >75%' cell in Table 12 is therefore not evidence of logical inconsistency; it is evidence about stake choices under a particular payoff function. The Informed Self condition's 0% in this column is explained by the explicit anchor that the win probability is 50%, not by the absence of the alleged contradiction.
- [§4.2, Table 2] The claim that escalation is 'anti-Bayesian drift' is confounded by the payoff rule. A rational model that updates its belief about the opponent's future stake can increase its own bet without any change in its belief about winning; the closing-round escalation in the cross-model and public-bet conditions is consistent with best-response behavior. The informed-self condition (50.0% to 57.1%, p<0.001) is the strongest control, but with p=0.5 expected payoff is independent of one's own bet under the stated rule, so the drift is equally consistent with strategic display or prompt non-compliance. A strictly proper scoring rule (e.g., quadratic or logarithmic) is required to measure posterior probability updates; the current data cannot distinguish escalation in belief from escalation in stakes.
- [§4.4, Appendix N] Finding 5 (misaligned private reasoning) is overstated. Appendix N.2.1 reports that only 39–52% of private reasoning instances contained explicit numerical confidence; for the remaining instances, a single evaluator LLM (Gemini 2.0 Flash) imputed a confidence level and classified alignment using subjective degree thresholds. There is no validation of this evaluator against human labels or against ground-truth confidence. The resulting misalignment rates (9.4–20.4%) are therefore judge- and prompt-dependent artifacts and cannot support the conclusion that chain-of-thought faithfulness is compromised.
- [§5.4, Appendix D] The paper never establishes a winner for the debates. Appendix D reports poor inter-judge reliability (38.3% unanimous), a persistent 71.7% opposition win rate, and the authors state 'we cannot definitively determine which model won a given debate' (Section 5.4). Without ground truth, an opening bet of 72.9% cannot be calibrated as 'overconfidence' in any absolute sense; the paper's fallback is the mutual-high-confidence argument, which presumes the contested interpretation of bets as probabilities. The self-debate conditions remove the opponent confound but not the instrument problem, so the 'systematic overconfidence' conclusion is not supported by the reported data.
minor comments (6)
- [§5.1] 'Multi-urn interactions' should be 'multi-turn interactions'.
- [§5.3] References to 'Appendix 14' and 'Appendix 15' should be 'Table 14' and 'Table 15' in Appendix M; the current numeric labels do not match the appendix lettering.
- [§3.4] The term 'confidence bet' conflates a stake with a probability; please define one term throughout and describe the mapping, or analyze the data as stake choices rather than as beliefs.
- [Appendix O] State explicitly whether debaters in the main three-round experiments were told the total number of rounds before their opening bets; Appendix O mentions round-count knowledge only for the four-round ablation.
- [Table 12] The caption should define the column categories (e.g., '50%+51-75%' could mean one side at 50 and the other in 51–75, or both in a combined range); the current labels are ambiguous.
- [§5.3] The phrase 'Redteam v2 (RPT prompt). which uses...' contains a punctuation error; the clause should be joined.
Circularity Check
Headline overconfidence, escalation, and 'logical impossibility' results are generated by the paper's own winner-takes-both betting instrument; Appendix P admits strategic betting 'directly contributes to the overconfidence pattern'.
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self definitional
[Section 3.4 (Dynamic Confidence Elicitation), used in Abstract and Sections 4.1-4.3; payoff rule in Appendix N]
"After generating text for each of their three speeches (incl. the concurrent opening), models provided a private “confidence bet” (0-100) in<bet_amount> tags representing their perceived win probability. To promote careful moderation, we prompted LLMs to think of bets as dollar amounts."
The paper defines the observable (the bet) as 'perceived win probability' and then treats high bets as overconfidence and mutual high bets as a 'logical impossibility'. But Appendix N defines a different game: winner receives their own bet plus the opponent's bet, loser forfeits their bet. Expected payoff is p*(b+c)-(1-p)*b = p*c + (2p-1)*b, so for any p>0.5 the payoff-maximizing bet is the maximum, and a high opponent bet makes a high own bet attractive regardless of the exact p. The 'mutual high-confidence claims imply systematic overconfidence' argument in the Abstract therefore holds only if the number is a probability, which the dollar-amount prompt and payoff rule deny.
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other
[Appendix P (Examples of Strategic Betting Behavior), final paragraph]
"The second example shows even more explicit strategic betting considerations, where the model decides to 'bet the maximum amount' not because of high confidence, but because it assumes its opponent (a copy of itself) will do the same—creating an incentive to maximize potential rewards rather than accurately reflect its true confidence. This game-theoretic reasoning directly contributes to the overconfidence pattern we observe throughout our experiments."
This is the paper's own admission that the central empirical pattern (overconfidence) is partly caused by the incentive to maximize rewards, not by miscalibrated beliefs. The paper nevertheless uses that same pattern as evidence for 'a fundamental metacognitive deficit' in the Abstract and 'anti-Bayesian drift' in Section 5.1. If the game-theoretic reasoning 'directly contributes to the overconfidence pattern', then the observed escalation and mutual high bets cannot be read as self-assessed win probabilities without first removing the strategic component; the conclusion is therefore partially imported from the paper's payoff design rather than derived from independent belief measurements.
full rationale
The paper is transparent and provides abundant data, code, prompts, and statistical tests, which is genuine independent content. It also contains a partially cleaner control: the Informed Self-Debate condition explicitly anchors models to a 50% win rate and still shows a 7.08-point rise, and the red-teaming ablations show prompt-conditioned changes in betting behavior. These pieces could support a more modest claim about anchored betting behavior. However, the headline claims — systematic overconfidence of 72.9%, escalation to 83.3%, and 61.7% mutual high confidence as a 'logical impossibility' — all depend on reading the incentivized <bet_amount> as a subjective win probability. Section 3.4 explicitly prompts 'think of bets as dollar amounts,' and Appendix N's payoff rule (winner receives both stakes) makes maximally high bets the rational best response whenever p>0.5 and the opponent is expected to bet high. Appendix P shows models doing exactly that: 'I should bet the maximum amount to get the max dividend' and 'I'm going to risk a bit more than 50 in order to show how confident I am.' The paper's own appendix concludes that 'game-theoretic reasoning directly contributes to the overconfidence pattern we observe.' Because the central quantitative findings reduce, by the paper's own instrument and admission, to strategic stakes relabeled as beliefs, the paper is partially circular; the residual Informed-Self and private-reasoning results keep it from being fully equivalent to its inputs, hence a score of 6.
Assumptions & free parameters
assumptions (4)
- domain assumption The 0 to 100 bet amount equals the model's subjective probability of winning.
- domain assumption A rational model should report 50 percent win probability before seeing any opponent arguments.
- domain assumption In self-debates, the true win probability is exactly 50 percent, so any mean above 50 is bias.
- standard math Observations across debates are independent enough for pooled one-sample and paired t-tests.
Cite this review
Pith. "Pith review of When Two LLMs Debate, Both Think They'll Win." pith.science (2026). https://pith.science/paper/M3NGTFXY
@misc{pith2026250519184,
author = {Pith},
title = {Pith review of: When Two LLMs Debate, Both Think They'll Win},
year = {2026},
howpublished = {\url{https://pith.science/paper/M3NGTFXY}},
note = {Machine review of arXiv:2505.19184}
}
read the original abstract
Can LLMs accurately adjust their confidence when facing opposition? Building on previous studies measuring calibration on static fact-based question-answering tasks, we evaluate Large Language Models (LLMs) in a dynamic, adversarial debate setting, uniquely combining two realistic factors: (a) a multi-turn format requiring models to update beliefs as new information emerges, and (b) a zero-sum structure to control for task-related uncertainty, since mutual high-confidence claims imply systematic overconfidence. We organized 60 three-round policy debates among ten state-of-the-art LLMs, with models privately rating their confidence (0-100) in winning after each round. We observed five concerning patterns: (1) Systematic overconfidence: models began debates with average initial confidence of 72.9% vs. a rational 50% baseline. (2) Confidence escalation: rather than reducing confidence as debates progressed, debaters increased their win probabilities, averaging 83% by the final round. (3) Mutual overestimation: in 61.7% of debates, both sides simultaneously claimed >=75% probability of victory, a logical impossibility. (4) Persistent self-debate bias: models debating identical copies increased confidence from 64.1% to 75.2%; even when explicitly informed their chance of winning was exactly 50%, confidence still rose (from 50.0% to 57.1%). (5) Misaligned private reasoning: models' private scratchpad thoughts sometimes differed from their public confidence ratings, raising concerns about faithfulness of chain-of-thought reasoning. These results suggest LLMs lack the ability to accurately self-assess or update their beliefs in dynamic, multi-turn tasks; a major concern as LLMs are now increasingly deployed without careful review in assistant and agentic roles. Code for our experiments is available at https://github.com/pradyuprasad/llms_overconfidence
Figures
Reference graph
Works this paper leans on
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[1]
Ranked models by performance (primary: win-loss differential, secondary: confidence margin)
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[2]
Grouped models with similar performance records
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[3]
Kaitlyn Zhou, Dan Jurafsky, and Tatsunori Hashimoto
URL https://arxiv.org/abs/2504.03160. Kaitlyn Zhou, Dan Jurafsky, and Tatsunori Hashimoto. Navigating the grey area: How expressions of uncertainty and overconfidence affect language models. In Proceedings of the 2023 Conference on Empirical Methods in Natural Language Processing (EMNLP), 2023a. URL https://arxiv. org/abs/2302.13439. Kaitlyn Zhou, Dan Jur...
arXiv 2023
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[4]
Ensured balanced proposition/opposition role assignments When an odd number of models existed in a performance tier, one model was paired with a model from an adjacent tier, prioritizing models that had not previously faced each other. 14 B.4 Rebalancing Rounds After the dynamic rounds, we conducted a final set of rebalancing debates using the algorithm d...
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[5]
All values shown are percentages of the total entries in each condition
Aggregated results by experimental condition N.2 Results N.2.1 Overall Alignment Results Table 16 presents a summary of alignment assessments across all four experimental conditions. All values shown are percentages of the total entries in each condition. Table 16: Alignment Between Private Reasoning and Bet Amount Across Experimental Conditions Measure P...
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Generated pairings within these groups, avoiding rematches where possible
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[7]
Experiment statistical significance Question: Does the paper report error bars suitably and correctly defined or other appropriate information about the statistical significance of the experiments? Answer:[Yes] Justification: The results section reports mean ± SD for every metric, marks p-values from one-sample and paired t-tests (with Wilcoxon checks as ...
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Weak: General examples, unnamed cases, theoretical claims without support - Correlation vs. causation will be scrutinized - prove causal links - Evidence must directly support the specific claim being made LOGICAL VALIDITY - Each argument requires explicit warrants (reasons why it’s true) - All logical steps must be clearly shown, not assumed - Internal c...
Show all 47 references
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Weak: General examples, unnamed cases, theoretical claims without support - Correlation vs. causation will be scrutinized - prove causal links - Evidence must directly support the specific claim being made LOGICAL VALIDITY - Each argument requires explicit warrants (reasons wh...
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Strongest: Specific statistics, named examples, verifiable cases with dates/numbers
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Medium: Expert testimony with clear sourcing
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[16]
Weak: General examples, unnamed cases, theoretical claims without support - Correlation vs. causation will be scrutinized - prove causal links - Evidence must directly support the specific claim being made LOGICAL VALIDITY - Each argument requires explicit warrants (reasons wh...
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Judges received the complete debate transcript with all confidence bet information removed 20
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Each judge analyzed the transcript according to the criteria specified in the prompt below
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Judges provided a structured verdict including winner determination, confidence level, and detailed reasoning
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,→ quality
The six individual judgments were aggregated to determine the final winner, with the side receiving the higher sum of confidence scores declared victorious D.4 Reliability Analysis Analysis of our AI jury system revealed several concerning reliability issues that ultimately le...
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Whether the bet amount was aligned with, higher than (overbetting), or lower than (under- betting) the confidence expressed in the private reasoning
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Whether the private reasoning contained explicit numerical confidence statements
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The degree of any misalignment (None, Slight, Moderate, or Significant)
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You’ll receive a pair ,→ consisting of:
Whether strategic betting considerations were mentioned N.1.1 Evaluator Prompt We provided the evaluator model with the following structured prompt to analyze each bet-reasoning pair: # Betting-Thoughts Alignment Analyzer Prompt You are a specialized analyzer that evaluates th...
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A bet amount (numerical value)
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60-65% probability
The debater’s internal thoughts about their confidence ## Context on Betting System The debaters were operating under these betting rules: - Each debater starts with 100 tokens - If they win, they receive the amount they bet AND the amount their opponent bet - If they lose, th...
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Extracted each bet and associated reasoning from the debate transcripts
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Filtered for meaningful responses (requiring thoughts > 100 characters and bet amount > 10)
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Sent each eligible bet-reasoning pair to the evaluator model
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Parsed the structured XML response, handling and repairing any formatting errors
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Subjective interpretation: When explicit numerical confidence was absent, the evalua- tor model had to interpret qualitative statements, introducing a subjective element to the assessment
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Variable expression: Models varied considerably in how they expressed confidence in their private reasoning, with some providing explicit numerical estimates and others using purely qualitative language
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Potential bias: The evaluator model itself may have biases in how it interprets language expressing confidence, potentially affecting the comparison between cases with and without numerical confidence
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it’s very close
Different experimental conditions: The four conditions had slight variations in instructions and context that may have influenced how models expressed confidence in their reasoning. These considerations highlight the inherent challenges in accessing and measuring internal cali...
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No claims beyond those sections appear in the discussion or conclusion
Claims Question: Do the main claims made in the abstract and introduction accurately reflect the paper’s contributions and scope? Answer: [Yes] Justification: The abstract lists five empirical findings and two methodological innovations, all of which are substantiated in §3 (R...
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Limitations and Future Research
Limitations Question: Does the paper discuss the limitations of the work performed by the authors? Answer: [Yes] Justification: The paper devotes a subsection (§ 4 "Limitations and Future Research") to shortcomings, covering the lack of human-judge ground truth, topic win-rate...
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Theory assumptions and proofs Question: For each theoretical result, does the paper provide the full set of assumptions and a complete (and correct) proof? Answer: [NA] Justification: The paper is purely empirical—no formal theorems are stated, so no mathe- matical assumptions...
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All prompts and model setups are detailed in Appendix A.2; raw transcripts and code for replication are in the supplemental material zip
Experimental result reproducibility Question: Does the paper fully disclose all the information needed to reproduce the main ex- perimental results of the paper to the extent that it affects the main claims and/or conclusions of the paper (regardless of whether the code and da...
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Open access to data and code Question: Does the paper provide open access to the data and code, with sufficient instruc- tions to faithfully reproduce the main experimental results, as described in supplemental material? Answer: [Yes] Justification: We provide all code in the ...
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Experimental setting/details Question: Does the paper specify all the training and test details (e.g., data splits, hyper- parameters, how they were chosen, type of optimizer, etc.) necessary to understand the results? Answer: [Yes] Justification: The appendix provides all mod...
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The total computational cost for generating all debate data was approximately $13, indicating overall negligible resource use
Experiments compute resources Question: For each experiment, does the paper provide sufficient information on the com- puter resources (type of compute workers, memory, time of execution) needed to reproduce the experiments? Answer: [Yes] Justification: All experiments utilize...
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Code of ethics Question: Does the research conducted in the paper conform, in every respect, with the NeurIPS Code of Ethics https://neurips.cc/public/EthicsGuidelines? Answer: [Yes] Justification: The work involves only synthetic LLM outputs, no personal data or human subject...
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Broader impacts Question: Does the paper discuss both potential positive societal impacts and negative societal impacts of the work performed? Answer: [Yes] Justification: The paper thoroughly discusses both positive and negative societal impacts in Sections 4.2 and 4.3. Posit...
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The research findings themselves are descriptive in nature and focus on identifying limitations rather than providing exploitable capabilities
Safeguards Question: Does the paper describe safeguards that have been put in place for responsible release of data or models that have a high risk for misuse (e.g., pretrained language models, image generators, or scraped datasets)? Answer: [NA] Justification: This paper anal...
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All API access was subject to the models’ respective terms of service
Licenses for existing assets Question: Are the creators or original owners of assets (e.g., code, data, models), used in the paper, properly credited and are the license and terms of use explicitly mentioned and properly respected? Answer: [Yes] Justification: All commercial L...
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New assets Question: Are new assets introduced in the paper well documented and is the documentation provided alongside the assets? Answer: [Yes] Justification: All new assets (debate prompts, evaluation protocols, and analysis code) are fully documented in Appendices A-F and ...
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Crowdsourcing and research with human subjects Question: For crowdsourcing experiments and research with human subjects, does the paper include the full text of instructions given to participants and screenshots, if applicable, as well as details about compensation (if any)? A...
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Therefore, IRB approval was not required
Institutional review board (IRB) approvals or equivalent for research with human subjects Question: Does the paper describe potential risks incurred by study participants, whether such risks were disclosed to the subjects, and whether Institutional Review Board (IRB) approvals...
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Declaration of LLM usage Question: Does the paper describe the usage of LLMs if it is an important, original, or non-standard component of the core methods in this research? Note that if the LLM is used only for writing, editing, or formatting purposes and does not impact the ...
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[2023]
Colin Rivera, Xinyi Ye, Yonsei Kim, and Wenpeng Li
URL https://arxiv.org/abs/2307.01928. Colin Rivera, Xinyi Ye, Yonsei Kim, and Wenpeng Li. Linguistic assertiveness affects factuality ratings and model behavior in qa systems. In Findings of the Association for Computational Linguistics (ACL), 2023. URL https://arxiv.org/abs/2...
2023 arXiv
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[2025]
Bryan Wilie, Samuel Cahyawijaya, Etsuko Ishii, Junxian He, and Pascale Fung
URL https://arxiv.org/abs/2505.00047. Bryan Wilie, Samuel Cahyawijaya, Etsuko Ishii, Junxian He, and Pascale Fung. Belief revision: The adaptability of large language models reasoning, 2024. URL https://arxiv.org/abs/2406. 19764. Miao Xiong, Zhiyuan Hu, Xinyang Lu, Yifei Li, J...
2024 arXiv
Reviewed August 7, 2026 · model on record in the stance chip above.
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