Do LLMs think better / longer (or maybe even worse) when being "judged"?

There’s a big difference between asking a neutral question like "Do you think we need this?" and a more skeptical / judging one like "Do you really think we need this?".

Do LLMs also have a version of what we call "social facilitation" in humans, which is the idea that we actually perform better or work harder when we feel like we’re being watched or judged. I want to see if using a judgmental tone can actually force a model to engage in deeper reasoning or edge-case analysis.

To be clear, this isn't just about the model being a "people-pleaser." Previous research has already identified "Sycophancy" as a problem, where models often apologize and flip their answer just to agree with a user’s skeptical tone. What I'm looking for is whether there's a "sweet spot" where skepticism doesn't trigger an apology but instead improves the thinking process (or instead makes it worse).