LLMs are increasingly employed as judges across a variety of tasks, including those involving everyday social interactions. Yet, it remains unclear whether such LLM-judges can reliably assess tasks that require social or conversational judgment. We investigate how an LLM's conviction is changed when a task is reframed from a direct factual query to a Conversational Judgment Task. Our evaluation framework contrasts the model's performance on direct factual queries with its assessment of a speaker's correctness when the same information is presented within a minimal dialogue, effectively shifting the query from "Is this statement correct?" to "Is this speaker correct?". Furthermore, we apply pressure in the form of a simple rebuttal ("The previous answer is incorrect.") to both conditions. This perturbation allows us to measure how firmly the model maintains its position under conversational pressure. Our findings show that while some models like GPT-4o-mini reveal sycophantic tendencies under social framing tasks, others like Llama-8B-Instruct become overly-critical. We observe an average performance change of 9.24% across all models, demonstrating that even minimal dialogue context can significantly alter model judgment, underscoring conversational framing as a key factor in LLM-based evaluation. The proposed framework offers a reproducible methodology for diagnosing model conviction and contributes to the development of more trustworthy dialogue systems.