Beyond Bias Scores: Answerability Confounds in Activation Steering with Gradient-Constrained Direction Design (GCD)

Multiple-choice question (MCQ) benchmarks are widely used to evaluate large language models, yet a single reported accuracy number is not enough to distinguish a model's latent ability from order sensitivity. Debiasing methods tend to be judged on one axis, which implicitly assumes that fixing order sensitivity and improving accuracy go together. We test this assumption with two proprietary models and two open-weight models on MMLU and ARC-Challenge, across four families of strategies. We measure order sensitivity with flip rate, capturing per-question instability, and recall standard deviation (RStd), capturing aggregate positional imbalance. We find accuracy and order sensitivity do not move together consistently: two-stage prompting reduces both flip rate and RStd for GPT on MMLU without a significant change in accuracy. The two sensitivity metrics also diverge from each other. Adding reasoning to direct answering leaves Llama's MMLU flip rate statistically indistinguishable while RStd falls sharply. A $2\times2$ ablation across generation-then-matching, crossing option visibility with matcher type, shows that withholding options mainly harms semantic matching, which achieves zero flip rate by construction, yet loses significantly in accuracy; the effect is smaller when using an LLM matcher. We recommend reporting flip rate and RStd along with accuracy when evaluating MCQ strategies.

A model should refuse two different things: answers it would get wrong, and questions it should not answer at all, such as unanswerable ones or ones resting on a false premise. The usual recipe thresholds a single confidence score, which cannot tell these apart. Across five instruction-tuned models from three families (2B to 14B), we find they are separate axes. Ordinary answer-confidence tracks whether an answer is right but is nearly blind to whether the question is answerable; a linear probe on hidden states does the reverse. The blind spot does not shrink with scale. It is worst on naturally occurring false-premise questions (CREPE). There, answer-confidence, P(IK), P(True), and even asking the model outright whether a premise is false all stay near chance, while a hidden-state probe reaches 0.69 to 0.77 AUROC: the model represents a problem it will not report. This turns out to be fixable. Instructing a model to check premises backfires, because it then disputes sound and false premises alike (57% false challenges), unable to tell them apart; routing the same instruction with the probe roughly triples challenge precision. We turn the two axes into a calibrated policy that answers only when an answerability score and a correctness score each clear a separately certifies behave differently: the unanswerable-answer rate is controllable at every scale, while the wrong-answer rate is capped by model accuracy, so the guarantee tightens as threshold policy certifies both budgets at 0.75 coverage of correct answers, against 0.31 for a single threshold; at 14B it is the only policy that certifies at all.

Standard language model evaluation assigns scores to single predicted answers, rewarding high-confidence responses regardless of how residual probability mass is distributed over alternative options. This creates a systematic pressure toward overconfident guessing: under accuracy-based schemes, a model maximises its expected score by always committing to an answer rather than abstaining, even when its uncertainty is high. While penalty-based approaches partially address this by raising the confidence threshold for strategic guessing, they still treat all sub-threshold responses identically, ignoring a fundamental distinction in how models can express uncertainty - for example between hedging toward incorrect answers versus hedging toward "I don't know" responses. This paper introduces a novel evaluation metric to solve this problem of not considering a model's entire probability distribution over answer choices. The metric naturally distinguishes between harmful overconfidence in wrong answers and uncertainty expressed through abstention, providing scores in an interpretable default range. Through theoretical analysis and illustrative examples, the metric is shown to offer a more nuanced and aligned evaluation paradigm that incentivises models to express genuine uncertainty rather than guessing. Adapting 12 existing evaluation benchmarks to the metric's variants and measuring performance on six language models shows that for half of the tested benchmarks scores are negative across all tested models, indicating significant tendencies towards hallucination.