Source-Aware Uncertainty Quantification for Decision-Making with Large Language Models

Making operational decisions under uncertainty is a central challenge in operations research. Large language models add a new difficulty: the decision problem itself may be ambiguous, vague, incomplete, inconsistent, or dependent on an unstated context. Yet existing uncertainty-quantification (UQ) methods primarily measure output probabilities or variation without identifying the source or appropriate intervention. We propose a source-aware, action-oriented taxonomy of input uncertainty distinguishing ambiguity, vagueness, underspecification, inconsistency, and context dependence. We construct a balanced 70-prompt container-terminal benchmark and evaluate twelve LM-Polygraph estimators on shared Qwen3-8B chat and thinking generations. Six probability-, entropy-, and lexical-based estimators nearly perfectly separate linguistic-source prompts from baseline in chat (macro-AUROC $0.994$--$1.000$). However, no chat-mode source-separability test survives multiplicity correction, while response length alone reaches macro-AUROC $0.982$. Detecting uncertainty-related output changes therefore does not establish source identification or intervention selection. Output-level UQ should complement explicit input-side diagnosis to make uncertainty actionable.