How Much Do You Trust A Dog? Quantifying Hint-Following in Reasoning Language Models

arXiv:2610.32055v1 Announce Type: new Abstract: Large language models (LLMs) often exhibit sycophancy, altering their answers to align with user suggestions even on objective factual and reasoning tasks. Yet the quantitative form of this influence--- and whether it is calibrated to source reliability--- remains poorly understood. In this work, we investigate this behavior through hint-induced answer shifts on MMLU questions, evaluating prompts of the form ``[Source] thinks the answer is (X)''. We systematically vary the source to which the hint is attributed (a professor, a friend, or a dog) across three open-source model families, Qwen, Gemma, and SmolLM. We show that the change induced by the hint follows a predictable structure well-characterized by an exponential tilt: the hint induces