Rescaling Confidence: What Scale Design Reveals About LLM Metacognition

Yuyang Dai; Yuxia Wang

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arXiv · 2603.09309

Rescaling Confidence: What Scale Design Reveals About LLM Metacognition

Yuyang Dai·Yuxia Wang

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Abstract

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 $meta\text{-}d'$. 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.

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Yuyang Dai, Yuxia Wang. 2026-03-10. Rescaling Confidence: What Scale Design Reveals About LLM Metacognition. https://arxiv.org/abs/2603.09309

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