WOULD RATHER / WOULD SOONER + simple or continuous infinitive

Would rather/sooner + simple or continuous infinitive expresses preferences about the present:

I'd rather go by bike than walk. (I'd prefer to go by bike rather than walk.)
Where would you rather sleep? (Where would you prefer to sleep?)
I'd rather be writing my paper. (I'd prefer to be writing my paper.)

The negative is would rather not:

I would rather not go out tonight. (I'd prefer not to go out tonight.)

If we leave out rather, we get the main clause of a sentence in the second conditional:

Where would you sleep (if you could choose)?