Permutation-Consensus Listwise Judging for Robust Factuality Evaluation

Abstract

Large language models (LLMs) are now widely used as judges, yet their decisions can change under presentation choices that should be irrelevant. We study one such source of instability: candidate-order sensitivity in listwise factuality evaluation, where several answers can look similarly polished while differing substantially in hallucination risk. We introduce PCFJudge, an inference-time method that reruns the same factuality-first listwise prompt over multiple orderings of the same candidate set and aggregates the resulting scores, ranks, and uncertainty signals into a single consensus decision. On RewardBench 2 Factuality, the final seven-permutation aggregate (K=7) improves top-1 selection accuracy from 86.00% to 91.33% with GPT-5.4 and from 86.33% to 89.67% with Claude Sonnet 4.6. These results suggest that candidate order can be a meaningful source of factuality-judging error and that marginalizing over this nuisance variation can improve the reliability of LLM evaluation.