Large language models (LLMs) are known to exhibit social sycophancy, often validating or agreeing with users in socially sensitive contexts. Existing evaluations typically measure sycophancy under a fixed prompt formulation, leaving unclear whether such behavior is stable when the same underlying situation is presented with different sycophancy-relevant prompt variants. In this work, we study sycophancy prompt sensitivity: the extent to which changes in user confidence, emotional framing, social consensus, or validation-seeking language alter a model's sycophantic behavior. We refer to our evaluation framework as SyPS, short for Sycophancy Prompt Sensitivity. Building on existing social sycophancy evaluation settings, SyPS constructs controlled prompt variants that preserve the same underlying user situation while varying sycophancy-relevant social cues. We introduce the Sycophancy Prompt Sensitivity Score (SPSS), an instance-level measure of sycophancy variation across paired prompt variants. Unlike aggregate sycophancy rates, SPSS separates baseline sycophancy from prompt-induced shifts, enabling model-level comparisons of robustness to sycophancy-relevant social cues. Empirically, we find that sycophancy prompt sensitivity is socially structured: validation-seeking and emotional-pressure cues often increase sycophancy, whereas counter-framing and anti-sycophancy prompts tend to reduce it. Our framework highlights whether LLMs maintain stable social judgments while adapting appropriately in tone.

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