Diagnosing LLM Arbitration Behavior over Pre-evidence Epistemic States in RAG-based Fact-Checking

In RAG-based fact-checking, LLMs are increasingly used as verifiers to check given claims against retrieved evidence. Their parametric knowledge can induce pre-evidence tendencies that may conflict with the retrieved context, yet existing evaluation frameworks do not characterize such prior-context discrepancy or measure how verifiers arbitrate between parametric and contextual signals. We introduce \textsc{PAVE} (\emph{Prior-Aware Verifier Evaluation}), a diagnostic testbed that stratifies an LLM verifier into four epistemic states based on the correctness and confidence of its pre-evidence prior and evaluates its arbitration behavior on this new benchmark, i.e., whether it persists in correct prior under misleading evidence, and whether it corrects wrong prior when accurate evidence is provided. Experiments across seven LLMs reveal unreliable and highly model-dependent prior-context arbitration, highlighting the importance of verifier selection for real-world RAG-based fact-checking applications. Based on these findings, we propose a lightweight JSD-based test-time arbitration method that improves factual reliability without modifying the underlying model, achieving competitive performance across diverse LLM families.