# Rescaling Confidence: What Scale Design Reveals About LLM Metacognition

arXiv: https://arxiv.org/abs/2603.09309 · HTML: https://mlsanity.com/paper/2603.09309/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 32 references that are in the map.
- First posted on arXiv 10 Mar 2026.

## Builds on (most cited first, 12 of 12)

- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [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)
- [TruthfulQA: Measuring How Models Mimic Human Falsehoods](https://mlsanity.com/paper/2109.07958/) (2021)
- [Language Models (Mostly) Know What They Know](https://mlsanity.com/paper/2207.05221/) (2022)
- [Calibrate Before Use: Improving Few-Shot Performance of Language Models](https://mlsanity.com/paper/2102.09690/) (2021)
- [Can LLMs Express Their Uncertainty? An Empirical Evaluation of Confidence Elicitation in LLMs](https://mlsanity.com/paper/2306.13063/) (2023)
- [Teaching Models to Express Their Uncertainty in Words](https://mlsanity.com/paper/2205.14334/) (2022)
- [Measuring Calibration in Deep Learning](https://mlsanity.com/paper/1904.01685/) (2019)
- [Verified Uncertainty Calibration](https://mlsanity.com/paper/1909.10155/) (2019)
- [Relying on the Unreliable: The Impact of Language Models' Reluctance to Express Uncertainty](https://mlsanity.com/paper/2401.06730/) (2024)

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

- [I-CALM: Incentivizing Confidence-Aware Abstention for LLM Selective Answering](https://mlsanity.com/paper/2604.03904/) (2026)
- [Beyond Confidence: Rethinking Self-Assessments for Performance Prediction in LLMs](https://mlsanity.com/paper/2605.07806/) (2026)
- [Rethinking Verbalized Confidence for LLM-as-a-Judge: A Compatibility Shift on Post-2025 Proprietary Models](https://mlsanity.com/paper/2609.10996/) (2026)

## Abstract (arXiv)

Verbalized confidence, in which LLMs report a numerical certainty score, is widely used to estimate uncertainty in black-box settings, yet the confidence scale itself (typically 0--100) is rarely examined. We show that this design choice is not neutral. Across six LLMs and three datasets, verbalized confidence is heavily discretized, with more than 78% of responses concentrating on just three round-number values. To investigate this phenomenon, we systematically manipulate confidence scales along three dimensions: granularity, boundary placement, and range regularity, and evaluate metacognitive sensitivity using meta-d'. We find that a 0--20 scale consistently improves metacognitive efficiency over the standard 0--100 format, while boundary compression degrades performance and round-number preferences persist even under irregular ranges. These results demonstrate that confidence scale design directly affects the quality of verbalized uncertainty and should be treated as a first-class experimental variable in LLM evaluation.