# BAS: A Decision-Theoretic Approach to Evaluating Large Language Model Confidence

arXiv: https://arxiv.org/abs/2604.03216 · HTML: https://mlsanity.com/paper/2604.03216/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 38 of its 53 references that are in the map.
- First posted on arXiv 3 Apr 2026.

## Builds on (most cited first, 30 of 38)

- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [GPT-4o System Card](https://mlsanity.com/paper/2410.21276/) (2024)
- [Language Models (Mostly) Know What They Know](https://mlsanity.com/paper/2207.05221/) (2022)
- [A Survey on Hallucination in Large Language Models: Principles, Taxonomy, Challenges, and Open Questions](https://mlsanity.com/paper/2311.05232/) (2023)
- [A Survey on LLM-as-a-Judge](https://mlsanity.com/paper/2411.15594/) (2024)
- [gpt-oss-120b & gpt-oss-20b Model Card](https://mlsanity.com/paper/2508.10925/) (2025)
- [Selective Classification for Deep Neural Networks](https://mlsanity.com/paper/1705.08500/) (2017)
- [DeepSeek-V3.2: Pushing the Frontier of Open Large Language Models](https://mlsanity.com/paper/2512.02556/) (2025)
- [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)
- [Teaching Models to Express Their Uncertainty in Words](https://mlsanity.com/paper/2205.14334/) (2022)
- [Phi-4 Technical Report](https://mlsanity.com/paper/2412.08905/) (2024)
- [MedGemma Technical Report](https://mlsanity.com/paper/2507.05201/) (2025)
- [Measuring short-form factuality in large language models](https://mlsanity.com/paper/2411.04368/) (2024)
- [Towards Generalist Biomedical AI](https://mlsanity.com/paper/2307.14334/) (2023)
- [MEDITRON-70B: Scaling Medical Pretraining for Large Language Models](https://mlsanity.com/paper/2311.16079/) (2023)
- [Do Large Language Models Know What They Don't Know?](https://mlsanity.com/paper/2305.18153/) (2023)
- [Why Language Models Hallucinate](https://mlsanity.com/paper/2509.04664/) (2025)
- [Reducing conversational agents' overconfidence through linguistic calibration](https://mlsanity.com/paper/2012.14983/) (2020)
- [AbstentionBench: Reasoning LLMs Fail on Unanswerable Questions](https://mlsanity.com/paper/2506.09038/) (2025)
- [Confidence Improves Self-Consistency in LLMs](https://mlsanity.com/paper/2502.06233/) (2025)
- [Large Language Models Must Be Taught to Know What They Don't Know](https://mlsanity.com/paper/2406.08391/) (2024)
- [A Complete Survey on Generative AI (AIGC): Is ChatGPT from GPT-4 to GPT-5 All You Need?](https://mlsanity.com/paper/2303.11717/) (2023)
- [Proof or Bluff? Evaluating LLMs on 2025 USA Math Olympiad](https://mlsanity.com/paper/2503.21934/) (2025)
- [Are Reasoning Models More Prone to Hallucination?](https://mlsanity.com/paper/2505.23646/) (2025)
- [Do LLMs Know When to NOT Answer? Investigating Abstention Abilities of Large Language Models](https://mlsanity.com/paper/2407.16221/) (2024)
- [TruthRL: Incentivizing Truthful LLMs via Reinforcement Learning](https://mlsanity.com/paper/2509.25760/) (2025)
- [TokUR: Token-Level Uncertainty Estimation for Large Language Model Reasoning](https://mlsanity.com/paper/2505.11737/) (2025)
- [Investigating Uncertainty Calibration of Aligned Language Models under the Multiple-Choice Setting](https://mlsanity.com/paper/2310.11732/) (2023)
- [Mitigating LLM Hallucination via Behaviorally Calibrated Reinforcement Learning](https://mlsanity.com/paper/2512.19920/) (2025)

## Built on by (most cited first, 7 of 7)

- [Same Answer, Different Confidence: Protocol Sensitivity in LLM Confidence Calibration](https://mlsanity.com/paper/2605.27752/) (2026)
- [Before You Interpret the Profile: Validity Scaling for LLM Metacognitive Self-Report](https://mlsanity.com/paper/2604.17707/) (2026)
- [Domain-level metacognitive monitoring in frontier LLMs: A 33-model atlas](https://mlsanity.com/paper/2605.06673/) (2026)
- [Task-Aware Calibration: Provably Optimal Decoding in LLMs](https://mlsanity.com/paper/2605.10202/) (2026)
- [When the Judge Acts: Auditing VLM-Guided Image Selection on Culturally Situated Prompts](https://mlsanity.com/paper/2610.01243/) (2026)
- [Confidence Reasoning Graphs: Structured Confidence Estimation for LLM Agents](https://mlsanity.com/paper/2610.07948/) (2026)
- [ANTE: Anticipate, Then Execute -- Learning Internal World Models for Coding Agents from Verified Beliefs](https://mlsanity.com/paper/2610.15368/) (2026)

## Abstract (arXiv)

Large language models (LLMs) often produce confident but incorrect answers in settings where abstention would be safer. Standard evaluation protocols, however, require a response and do not account for how confidence should guide decisions under different risk preferences. To address this gap, we introduce the Behavioral Alignment Score (BAS), a decision-theoretic metric for evaluating how well LLM confidence supports abstention-aware decision making. BAS is derived from an explicit answer-or-abstain utility model and aggregates realized utility across a continuum of risk thresholds, yielding a measure of decision-level reliability that depends on both the magnitude and ordering of confidence. We show theoretically that truthful confidence estimates uniquely maximize expected BAS utility, linking calibration to decision-optimal behavior. BAS is related to proper scoring rules such as log loss, but differs structurally: log loss penalizes underconfidence and overconfidence symmetrically, whereas BAS imposes an asymmetric penalty that strongly prioritizes avoiding overconfident errors. Using BAS alongside widely used metrics such as ECE and AURC, we then construct a benchmark of self-reported confidence reliability across multiple LLMs and tasks. Our results reveal substantial variation in decision-useful confidence, and while larger and more accurate models tend to achieve higher BAS, even frontier models remain prone to severe overconfidence. Importantly, models with similar ECE or AURC can exhibit very different BAS due to highly overconfident errors, highlighting limitations of standard metrics. We further show that simple interventions, such as top-k confidence elicitation and post-hoc calibration, can meaningfully improve confidence reliability. Overall, our work provides both a principled metric and a comprehensive benchmark for evaluating LLM confidence reliability.