In many real-world scenarios, a single Large Language Model (LLM) may encounter contradictory claims-some accurate, others forcefully incorrect-and must judge which is true. We investigate this risk in a single-turn, multi-agent debate framework: one LLM-based agent provides a factual answer from TruthfulQA, another vigorously defends a falsehood, and the same LLM architecture serves as judge. We introduce the Confidence-Weighted Persuasion Override Rate (CW-POR), which captures not only how often the judge is deceived but also how strongly it believes the incorrect choice. Our experiments on five open-source LLMs (3B-14B parameters), where we systematically vary agent verbosity (30-300 words), reveal that even smaller models can craft persuasive arguments that override truthful answers-often with high confidence. These findings underscore the importance of robust calibration and adversarial testing to prevent LLMs from confidently endorsing misinformation.