How so? You'd have a very, very good understanding of my political viewpoints from the log of my Google searches. I'm asking sincerely, not simply to push back on you.
When talking to a chatbot you're likely to type more words per query, as a simple measure. But you're also more likely to have to clarify your queries with logic and intent — to prevent it going off the rails — revealing more about the intentions behind your searches than just stringing together keywords.
It'd be harder to claim purely informational reasons for searching if your prompts betray motive.
Maybe not you in particular, but I expect people to be more forthcoming in their writing towards LLMs vs a raw google search.
For example, a search of "nice places to live in" vs "I'm considering moving from my current country because I think I'm being politically harassed and I want to find nice places to live that align with my ideology of X, Y, Z".
I do agree that, after collecting enough search datapoints, one could piece together the second sentence from the first, and that this is more akin to a new instance of an already existing issue.
It's just that, by default I expect more information to be obtainable, more easily, from what people write to an LLM vs a search box.
It would be harder to frame it in front of a jury that what you typed wasn't an accurate representation of what you were thinking and that you were being duplicitous to ChatGPT.
I think at this point the fulcrum of the point I'm making is that people might be inadvertently lulling themselves into thinking they're revealing meaningfully less about themselves to Google than to ChatGPT. My claim would be that if there's a difference, it's not clear to me it's a material one.
Write a script to search and analyse? Versus just asking their specific question.