Paper
Rescaling Confidence: What Scale Design Reveals About LLM Metacognition
Authors
Yuyang Dai
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-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.
Metadata
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Raw Data (Debug)
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"raw_xml": "<entry>\n <id>http://arxiv.org/abs/2603.09309v1</id>\n <title>Rescaling Confidence: What Scale Design Reveals About LLM Metacognition</title>\n <updated>2026-03-10T07:41:14Z</updated>\n <link href='https://arxiv.org/abs/2603.09309v1' rel='alternate' type='text/html'/>\n <link href='https://arxiv.org/pdf/2603.09309v1' rel='related' title='pdf' type='application/pdf'/>\n <summary>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.</summary>\n <category scheme='http://arxiv.org/schemas/atom' term='cs.AI'/>\n <published>2026-03-10T07:41:14Z</published>\n <arxiv:comment>18 pages, 5 figures</arxiv:comment>\n <arxiv:primary_category term='cs.AI'/>\n <author>\n <name>Yuyang Dai</name>\n </author>\n </entry>"
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