norwolf“
#1, I'd rather not stay here alone. = "I don't want to stay here alone." (Another option need not be explicit.)
#2, I wouldn't rather stay here alone. (The other option should be stated in prior context.)
Do they mean the same thing? In my opinion, they do not. ”
Regarding "rather" and "prefer," we always seem to be talking about a choice between two options, or in some cases, among more than two.
The options may be listed, or stated; but in some cases only one option is stated. (Of course, options may be stated in prior context.) When two options are not stated, we assume the second option to be the opposite, or the negative of the one which is stated.
The controversy here seems to surround the way we express this negative/opposite choice. Shall we say,
I do choose to not do X ?
I do not choose to do X ?
I do choose to do not X ?
You had better not do X
You had not better do X (You hadn't better do X)
I would rather not have an apple
I would not rather have an apple (I wouldn't rather have an apple)
I do not prefer to have an apple (I don't prefer to have an apple)
I do not choose to have an apple
I do not wish to have an apple
I wish not to have an apple
I prefer not to have an apple
I prefer to not have an apple
Anyway, I guess my point is that "rather" and "prefer" are different from all the others in this respect:
It's not idiomatic to place the "not" in front of them. If you do, you're deliberately making a play on words.
If someone hands you an apple and says, "Here's an apple for you,"
It's natural to say:
I do not choose/wish to have an apple.
It's unnatural to say:
I do not prefer to have an apple.
I would not rather have an apple.
These are humorous ways of saying, "I opt for the other choice." They may make an oblique comment on your feelings about apples: "I really hate apples!"