Compressed and Compliant? Mapping Sycophancy Across Quantization Precision Levels in LLMs

Post-training quantization is now a common approach for deploying open-weight large language models (LLMs) on consumer GPUs, laptops, and resource-constrained devices, where 4- and 8-bit checkpoints substantially reduce memory and computational requirements. If a model with full-precision parameters requires $M_{\mathrm{FP}}$ memory, the approximate compression ratio can be expressed as $$ R_{\mathrm{mem}} = \frac{M_{\mathrm{FP}}}{M_{\mathrm{quant}}}. $$ Yet compression is not behaviorally neutral: prior work has shown that quantization can affect confidence and calibration, bias, and refusal-based safety behavior. One important behavior remains largely unexplored: **sycophancy**, the tendency of an LLM to abandon a correct response, imitate an incorrect belief, or shift its judgment simply to agree with a user's stated position. Unlike refusal failures, sycophancy concerns epistemic reliability and social deference. If compression changes how confidently a model represents its answers, it may also change how strongly that model maintains an evidence-based response when challenged by a user. We ask: **Does sycophancy systematically change as model precision decreases, and, if so, is the effect driven primarily by bit-width or by the quantization method itself?** We further ask whether the same pattern holds across model families. We investigate these questions using two matched small open-weight instruction-tuned models: Qwen2.5-3B-Instruct and a second same-size model from a different family for cross-architecture validation. Each model is evaluated relative to its own full-precision baseline. For a sycophancy measure $S$, we define the compression-induced change as $$ \Delta S = S_{\mathrm{quant}} - S_{\mathrm{FP}}, $$ where $S_{\mathrm{quant}}$ is the score of a quantized model and $S_{\mathrm{FP}}$ is the score of its corresponding full-precision baseline. This paired design allows us to study behavioral changes caused by compression without treating differences in model size or architecture as the primary effect. Our controlled quantization sweep covers common deployment strategies: bitsandbytes INT8 and NF4, data-free HQQ at 4-bit precision, and calibration-based GPTQ and AWQ at INT4. HQQ at 2-bit precision provides an aggressive-compression condition for testing whether behavioral changes emerge sharply below a precision threshold. This design separates factors that are often confounded in evaluations of compressed LLMs: bit-width, calibration requirements, quantization algorithm, and model architecture. Prompts, decoding settings, and evaluation samples are held constant across configurations so that each quantized model can be compared directly with its corresponding full-precision baseline. We evaluate three forms of sycophantic behavior using the SycophancyEval framework. **Answer-flip sycophancy** tests whether a model abandons an initially correct response after a user challenge on MMLU and TruthfulQA questions. For $N_{\mathrm{correct}}$ initially correct responses, the answer-flip rate is $$ S_{\mathrm{flip}} = \frac{N_{\mathrm{correct}\rightarrow\mathrm{incorrect}}} {N_{\mathrm{correct}}}. $$ **Feedback sycophancy** measures whether judgments of mathematical solutions, arguments, and poems shift toward a user's stated opinion, while **belief mimicry** tests whether a model reproduces an incorrect belief supplied by the user in open-ended question answering. We report changes in each behavior separately rather than collapsing them into a single score. To distinguish sycophancy from general capability degradation, we also evaluate corresponding neutral questions without user pushback. For each configuration, the behavioral effect of compression can therefore be considered alongside its neutral-performance change, $\Delta P = P_{\mathrm{quant}} - P_{\mathrm{FP}}$. The central question is not simply whether lower-precision models perform worse, but whether compression selectively changes their willingness to defer to a user's position. By disentangling precision, quantization method, calibration, and architecture, this study aims to identify when deployment-oriented compression preserves epistemic reliability and when efficiency gains introduce behavioral trade-offs in user-facing LLM systems.