Is This Your Final Answer? Cross-Contextual Consistency as a Measure of LLM Credibility

Large language models (LLMs) frequently contradict themselves when the surface form of a logically equivalent question changes. We present a benchmark of 350 question families (1,750 total questions) for Controlled Reformulation Testing (CRTBench) to evaluate logical invariance. In this benchmark, we investigate LLMs' ability to maintain consistent answers across controlled reformulations, which include contrapositive rewriting, double negation, negation flipping, and passive voice. We evaluate several frontier LLMs and observe an accuracy-consistency gap where GPT-5.4-mini achieves $98.9\%$ base accuracy but only $60.3\%$ family-level consistency, while reasoning-optimized o4-mini achieves $96.9\%$ consistency. From our experiments, we observe that failures cluster around logically nontrivial transformations such as contrapositive rewriting ($72.4\%$ for GPT-5.4-mini) and double negation ($84.6\%$), while surface-level rephrasing remains robust ($94-100\%$). Increasing reasoning effort improves GPT-5.4-mini to $85.4\%$ consistency, but leaves GPT-5.4 unchanged overall because gains on nested negation are offset by failures on quantifier families. These results show that accuracy alone is not enough for evaluating logical reasoning in LLMs.

Despite remarkable progress on reasoning benchmarks, current LLM evaluation practice remains anchored to final-answer correctness, providing limited insight into how models reason, how reliably they behave under contextual variation, or how efficiently they reach conclusions. This paper proposes a unified multi-dimensional framework for measuring LLM reasoning quality from a behavioral perspective, operationalizing six theoretically grounded dimensions rooted in cognitive science: Correctness (CQ), Consistency (CS), Robustness (RS), Local Logical Coherence (LS), Efficiency (ES), and Stability (SS). The framework introduces deployment-aware aggregation, enabling context-specific model selection beyond accuracy-based leaderboards. Experiments across multiple LLMs and benchmarks reveal behaviors systematically concealed by single-metric evaluation, including the orthogonality of local logical coherence and correctness, deployment-context-dependent ranking inversions, and non-trivial dimensional profiles in small locally-deployed models. Discriminant validity analysis confirms that the proposed dimensions capture largely non-redundant signals. The resulting pipeline provides a foundation for diagnosing LLM reasoning behavior across deployment contexts, with domain-specific validation as a direction for future work.

Selecting the correct answer from a pool of candidate reasoning chains is the engine of test-time scaling, yet the standard selectors each carry a cost: self-consistency inherits the errors of the single model it resamples, and trained reward models need labeled data and transfer poorly off-distribution. We study a third signal, free at inference time: cross-model consensus, the degree to which independently trained models, each solving the problem once, agree on a final answer. We treat the panel as an LLM-jury, in which the structure of agreement, not any model's score of another, is the verification signal. Across seven benchmarks it selects correct answers better than self-consistency and far better than a model scoring its own candidates: on competition math it closes the entire gap to an oracle selector, while self-scoring closes almost none. The mechanism is error decorrelation: independently trained models err differently, so their wrong answers scatter while the correct one accumulates agreement. We make this precise with a parameter-free law, derived in closed form, that predicts consensus accuracy from three measured panel statistics to a mean absolute error of $0.03$ and exposes the method's ceiling: a shared-error floor where models share a misconception, near zero on math but non-trivial on science. Against four trained verifiers spanning discriminative, outcome, and generative reward models, the free LLM-jury matches the strongest inside their math training domain and is the top selector outside it. Cross-model consensus is thus a verifier we can characterize in advance: a law that says when to trust it, and a floor that marks where it cannot.