# When Two LLMs Debate, Both Think They'll Win

arXiv: https://arxiv.org/abs/2505.19184 · HTML: https://mlsanity.com/paper/2505.19184/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Placed in Reasoning for agents, planning and code, one of 17 directions in LLM reasoning.
- Builds on 29 of its 43 references that are in the map.
- First posted on arXiv 25 May 2025.

## Placed in

- LLM reasoning / [Reasoning for agents, planning and code](https://mlsanity.com/lr/reasoning-for-agents-planning-and-code/)

## Builds on (most cited first, 29 of 29)

- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [Language Models (Mostly) Know What They Know](https://mlsanity.com/paper/2207.05221/) (2022)
- [Understanding R1-Zero-Like Training: A Critical Perspective](https://mlsanity.com/paper/2503.20783/) (2025)
- [Can LLMs Express Their Uncertainty? An Empirical Evaluation of Confidence Elicitation in LLMs](https://mlsanity.com/paper/2306.13063/) (2023)
- [Just Ask for Calibration: Strategies for Eliciting Calibrated Confidence Scores from Language Models Fine-Tuned with Human Feedback](https://mlsanity.com/paper/2305.14975/) (2023)
- [Measuring Faithfulness in Chain-of-Thought Reasoning](https://mlsanity.com/paper/2307.13702/) (2023)
- [AI safety via debate](https://mlsanity.com/paper/1805.00899/) (2018)
- [Robots That Ask For Help: Uncertainty Alignment for Large Language Model Planners](https://mlsanity.com/paper/2307.01928/) (2023)
- [DeepResearcher: Scaling Deep Research via Reinforcement Learning in Real-world Environments](https://mlsanity.com/paper/2504.03160/) (2025)
- [Do LLMs exhibit human-like response biases? A case study in survey design](https://mlsanity.com/paper/2311.04076/) (2023)
- [Taming Overconfidence in LLMs: Reward Calibration in RLHF](https://mlsanity.com/paper/2410.09724/) (2024)
- [Which Economic Tasks are Performed with AI? Evidence from Millions of Claude Conversations](https://mlsanity.com/paper/2503.04761/) (2025)
- [Navigating the Grey Area: How Expressions of Uncertainty and Overconfidence Affect Language Models](https://mlsanity.com/paper/2302.13439/) (2023)
- [Are DeepSeek R1 And Other Reasoning Models More Faithful?](https://mlsanity.com/paper/2501.08156/) (2025)
- [Reasoning Models Better Express Their Confidence](https://mlsanity.com/paper/2505.14489/) (2025)
- [Privacy Issues in Large Language Models: A Survey](https://mlsanity.com/paper/2312.06717/) (2023)
- [Scalable AI Safety via Doubly-Efficient Debate](https://mlsanity.com/paper/2311.14125/) (2023)
- [Base Models Beat Aligned Models at Randomness and Creativity](https://mlsanity.com/paper/2505.00047/) (2025)
- [Beyond Semantics: The Unreasonable Effectiveness of Reasonless Intermediate Tokens](https://mlsanity.com/paper/2505.13775/) (2025)
- [Mind the Confidence Gap: Overconfidence, Calibration, and Distractor Effects in Large Language Models](https://mlsanity.com/paper/2502.11028/) (2025)
- [Uncertainty of Thoughts: Uncertainty-Aware Planning Enhances Information Seeking in Large Language Models](https://mlsanity.com/paper/2402.03271/) (2024)
- [Belief Revision: The Adaptability of Large Language Models Reasoning](https://mlsanity.com/paper/2406.19764/) (2024)
- [Language Models Fail to Introspect About Their Knowledge of Language](https://mlsanity.com/paper/2503.07513/) (2025)
- [Introspective Planning: Aligning Robots' Uncertainty with Inherent Task Ambiguity](https://mlsanity.com/paper/2402.06529/) (2024)
- [Active Task Disambiguation with LLMs](https://mlsanity.com/paper/2502.04485/) (2025)
- [When Persuasion Overrides Truth in Multi-Agent LLM Debates: Introducing a Confidence-Weighted Persuasion Override Rate (CW-POR)](https://mlsanity.com/paper/2504.00374/) (2025)
- [Controllable Light Diffusion for Portraits](https://mlsanity.com/paper/2305.04745/) (2023)
- [Learning from Failures in Multi-Attempt Reinforcement Learning](https://mlsanity.com/paper/2503.04808/) (2025)
- [Perspective Transition of Large Language Models for Solving Subjective Tasks](https://mlsanity.com/paper/2501.09265/) (2025)

## Built on by (most cited first, 10 of 10)

- [Interaction Protocol Shapes Moral Judgment in Multi-Agent Debate](https://mlsanity.com/paper/2510.10002/) (2025)
- [Shall We Play a Game? Language Models for Open-ended Wargames](https://mlsanity.com/paper/2509.17192/) (2025)
- [CRAwDAD: Causal Reasoning Augmentation with Dual-Agent Debate](https://mlsanity.com/paper/2511.22854/) (2025)
- [What LLM Agents Say When No One Is Watching: Social Structure and Latent Objective Emergence in Multi-Agent Debates](https://mlsanity.com/paper/2607.02507/) (2026)
- [Metacognition in LLMs: Foundations, Progress, and Opportunities](https://mlsanity.com/paper/2607.11881/) (2026)
- [MEDLEY-BENCH: Benchmarking Behavioural Metacognition and Belief Revision Under Social Pressure in Large Language Models](https://mlsanity.com/paper/2604.16009/) (2026)
- [Group Perspective Matters: Regulating Debate Relationships Can Mitigate Blind Conformity in Multi-Agent Debate](https://mlsanity.com/paper/2608.03648/) (2026)
- [From Prompting to Behavioral Alignment: Personalized LLM Judges for Recommendation Evaluation](https://mlsanity.com/paper/2608.11493/) (2026)
- [Measuring AI Accountability Through Argumentation Analysis: Can Model Reasoning Withstand Scrutiny?](https://mlsanity.com/paper/2609.05088/) (2026)
- [Measuring Collapse and Correction in Homogeneous-Panel LLM Debate](https://mlsanity.com/paper/2609.35279/) (2026)

## Abstract (arXiv)

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