When Text and Numbers Disagree: Evidence Arbitration in Large Language Models

Large language models (LLMs) are increasingly used in settings where textual summaries, numerical observations, and external tool outputs may provide conflicting evidence. We study how LLMs arbitrate between such sources when they support opposing decisions. To do so, we introduce a controlled synthetic benchmark in which latent risk trajectories generate both numerical time series and natural language summaries, allowing us to construct conflicts where exactly one evidence source is aligned with the ground-truth label. This design lets us independently manipulate modality, temporal recency, source reliability, and evidence provenance. Across open-weight instruction-tuned models, we find that arbitration behaviour is systematic rather than random: models exhibit distinct text-versus-number preferences, follow temporal recency more consistently than explicit reliability cues, and can over-rely on external forecasts even when they conflict with direct contextual evidence. These results suggest that current LLMs often rely on heuristic arbitration strategies when integrating heterogeneous evidence, highlighting a failure mode for tool-augmented decision systems.

BAS: A Decision-Theoretic Approach to Evaluating Large Language Model Confidence

Large language models (LLMs) often produce confident but incorrect answers in settings where abstention would be safer. Standard evaluation protocols, however, require a response and do not account for how confidence should guide decisions under different risk preferences. To address this gap, we introduce the Behavioral Alignment Score (BAS), a decision-theoretic metric for evaluating how well LLM confidence supports abstention-aware decision making. BAS is derived from an explicit answer-or-abstain utility model and aggregates realized utility across a continuum of risk thresholds, yielding a measure of decision-level reliability that depends on both the magnitude and ordering of confidence. We show theoretically that truthful confidence estimates uniquely maximize expected BAS utility, linking calibration to decision-optimal behavior. BAS is related to proper scoring rules such as log loss, but differs structurally: log loss penalizes underconfidence and overconfidence symmetrically, whereas BAS imposes an asymmetric penalty that strongly prioritizes avoiding overconfident errors. Using BAS alongside widely used metrics such as ECE and AURC, we then construct a benchmark of self-reported confidence reliability across multiple LLMs and tasks. Our results reveal substantial variation in decision-useful confidence, and while larger and more accurate models tend to achieve higher BAS, even frontier models remain prone to severe overconfidence. Importantly, models with similar ECE or AURC can exhibit very different BAS due to highly overconfident errors, highlighting limitations of standard metrics. We further show that simple interventions, such as top-$k$ confidence elicitation and post-hoc calibration, can meaningfully improve confidence reliability. Overall, our work provides both a principled metric and a comprehensive benchmark for evaluating LLM confidence reliability.

Entropy Alone is Insufficient for Safe Selective Prediction in LLMs

Selective prediction systems can mitigate harms resulting from language model hallucinations by abstaining from answering in high-risk cases. Uncertainty quantification techniques are often employed to identify such cases, but are rarely evaluated in the context of the wider selective prediction policy and its ability to operate at low target error rates. We identify a model-dependent failure mode of entropy-based uncertainty methods that leads to unreliable abstention behaviour, and address it by combining entropy scores with a correctness probe signal. We find that across three QA benchmarks (TriviaQA, BioASQ, MedicalQA) and four model families, the combined score generally improves both the risk--coverage trade-off and calibration performance relative to entropy-only baselines. Our results highlight the importance of deployment-facing evaluation of uncertainty methods, using metrics that directly reflect whether a system can be trusted to operate at a stated risk level.

Semantic Self-Distillation for Language Model Uncertainty

Large language models present challenges for principled uncertainty quantification, in part due to their complexity and the diversity of their outputs. Semantic dispersion, or the variance in the meaning of sampled answers, has been proposed as a useful proxy for model uncertainty, but the associated computational cost prohibits its use in latency-critical applications. We show that sampled semantic distributions can be distilled into lightweight student models which estimate a prompt-conditioned uncertainty before the language model generates an answer token. The student model predicts a semantic distribution over possible answers; the entropy of this distribution provides an effective uncertainty signal for hallucination prediction, and the probability density allows candidate answers to be evaluated for reliability. On TriviaQA, our student models match or outperform finite-sample semantic dispersion for hallucination prediction and provide a strong signal for out-of-domain answer detection. We term this technique Semantic Self-Distillation (SSD), which we suggest provides a general framework for distilling predictive uncertainty in complex output spaces beyond language.