# Evaluating and Calibrating LLM Confidence on Questions with Multiple Correct Answers

arXiv: https://arxiv.org/abs/2602.07842 · HTML: https://mlsanity.com/paper/2602.07842/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 39 references that are in the map.
- First posted on arXiv 8 Feb 2026.

## Builds on (most cited first, 23 of 23)

- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [GPT-4o System Card](https://mlsanity.com/paper/2410.21276/) (2024)
- [HotpotQA: A Dataset for Diverse, Explainable Multi-hop Question Answering](https://mlsanity.com/paper/1809.09600/) (2018)
- [TruthfulQA: Measuring How Models Mimic Human Falsehoods](https://mlsanity.com/paper/2109.07958/) (2021)
- [G-Eval: NLG Evaluation using GPT-4 with Better Human Alignment](https://mlsanity.com/paper/2303.16634/) (2023)
- [Language Models (Mostly) Know What They Know](https://mlsanity.com/paper/2207.05221/) (2022)
- [FEVER: a large-scale dataset for Fact Extraction and VERification](https://mlsanity.com/paper/1803.05355/) (2018)
- [FActScore: Fine-grained Atomic Evaluation of Factual Precision in Long Form Text Generation](https://mlsanity.com/paper/2305.14251/) (2023)
- [A General Language Assistant as a Laboratory for Alignment](https://mlsanity.com/paper/2112.00861/) (2021)
- [Can LLMs Express Their Uncertainty? An Empirical Evaluation of Confidence Elicitation in LLMs](https://mlsanity.com/paper/2306.13063/) (2023)
- [On Faithfulness and Factuality in Abstractive Summarization](https://mlsanity.com/paper/2005.00661/) (2020)
- [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)
- [How Can We Know When Language Models Know? On the Calibration of Language Models for Question Answering](https://mlsanity.com/paper/2012.00955/) (2020)
- [Calibration of Pre-trained Transformers](https://mlsanity.com/paper/2003.07892/) (2020)
- [Prompting GPT-3 To Be Reliable](https://mlsanity.com/paper/2210.09150/) (2022)
- [Out-of-Distribution Detection and Selective Generation for Conditional Language Models](https://mlsanity.com/paper/2209.15558/) (2022)
- [WiCE: Real-World Entailment for Claims in Wikipedia](https://mlsanity.com/paper/2303.01432/) (2023)
- [Calibrating Large Language Models with Sample Consistency](https://mlsanity.com/paper/2402.13904/) (2024)
- [When Do LLMs Need Retrieval Augmentation? Mitigating LLMs' Overconfidence Helps Retrieval Augmentation](https://mlsanity.com/paper/2402.11457/) (2024)
- [Towards Fully Exploiting LLM Internal States to Enhance Knowledge Boundary Perception](https://mlsanity.com/paper/2502.11677/) (2025)

## Built on by (most cited first, 3 of 3)

- [Seeing Before Agreeing: Aligning Multi-Agent Consensus with Visual Evidence](https://mlsanity.com/paper/2605.30698/) (2026)
- [Can LLM Rerankers Predict Their Own Ranking Performance?](https://mlsanity.com/paper/2606.03535/) (2026)
- [Assessing and Mitigating Miscalibration in LLM-Based Social Science Measurement](https://mlsanity.com/paper/2605.11954/) (2026)

## Abstract (arXiv)

Confidence calibration is essential for making large language models (LLMs) reliable, yet existing training-free methods have been primarily studied under single-answer question answering. In this paper, we show that these methods break down in the presence of multiple valid answers, where disagreement among equally correct responses leads to systematic underestimation of confidence. To enable a systematic study of this phenomenon, we introduce MACE, a benchmark of 12,000 factual questions spanning six domains with varying numbers of correct answers. Experiments across 15 representative calibration methods and four LLM families (7B-72B) reveal that while accuracy increases with answer cardinality, estimated confidence consistently decreases, causing severe miscalibration for questions with mixed answer counts. To address this issue, we propose Semantic Confidence Aggregation (SCA), which aggregates confidence over multiple high-probability sampled responses. SCA achieves state-of-the-art calibration performance under mixed-answer settings while preserving strong calibration on single-answer questions.