Rescaling Confidence: What Scale Design Reveals About LLM Metacognition

TL;DR

This paper investigates how the design of confidence scales affects the accuracy of LLMs' self-reported uncertainty, revealing that smaller, well-structured scales improve metacognitive sensitivity.

Contribution

It systematically examines the impact of confidence scale design on LLM metacognition, highlighting the importance of scale granularity and boundaries.

Findings

0-20 scale improves metacognitive efficiency

Boundary compression degrades performance

Round-number preferences persist despite irregular ranges

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.