Rescaling Confidence: What Scale Design Reveals About LLM Metacognition

The numerical scale used to prompt large language models for confidence scores is not a neutral design choice, according to a new study. Researchers found that the standard 0–100 scale leads to heavily discretized responses, with a compressed 0–20 scale consistently improving metacognitive efficiency across multiple models and datasets [1][2]. The study, posted on the arXiv preprint server and revised on June 15, 2026, systematically manipulated confidence scales along three dimensions: granularity, boundary placement, and range regularity [1][2]. The authors, including Yuyang Dai, evaluated metacognitive sensitivity using a metric called meta-d' [1][2]. They found that verbalized confidence under the typical 0–100 format is heavily discretized, with more than 78% of responses concentrating on just three round-number values [1][2]. This round-number preference persisted even under irregular ranges [2]. Boundary compression, another design factor, degraded metacognitive performance [1][2]. The findings suggest that the quality of verbalized uncertainty is directly affected by scale design and should be treated as a first-class experimental variable in LLM evaluation [1][2]. The paper was submitted on March 10, 2026, with an initial file size of 232 KB, and the revised version was 222 KB [1]. The work appears within the broader context of arXiv, an open-access repository of electronic preprints that is not peer-reviewed but is moderated [6]. Founded in 1991, arXiv hosts scientific papers across fields including computer science, physics, and mathematics, and as of November 2024 receives about 24,000 submissions per month [6]. The study is accessible through arXiv's abstract page, which features experimental community tools under the arXivLabs framework [3][4]. arXivLabs, launched as a formalized framework in 2020, allows community collaborators to develop and share new features directly on the site, such as the Bibliographic Explorer and CORE Recommender [4][5]. "Members of our community want to contribute tools that enhance the arXiv experience, and we value that kind of community engagement," said Eleonora Presani, arXiv Executive Director, at the time of the launch [4]. The framework operates under values of openness, community, excellence, and user data privacy [4]. arXiv is currently pausing new Labs proposals while its development team focuses on modernizing and moving systems to the cloud [3].