This point confused me for awhile. Here's what I've found in 'A Practical English Grammar':
would rather/sooner and prefer/would prefer
There is no difference between would rather and would sooner, but would rather is more often heard.
A) would rather/sooner is followed by the bare infinitive when the subject of would rather/sooner is the same as the subject of the following action:
Tom would rather read than talk.
В Subject + would rather/sooner is followed by subject + past tense (subjunctive) when the two subjects are different:
Shall I give you a cheque? ~ I’d rather you paid cash.
Note the use of would rather + subject + didn’t for a negative preference:
Would you like him to paint it? ~ No, I’d rather he didn’t (paint it).
Ann wants to tell Tom, but I’d rather she didn’t (tell him).
And in 'Practical English Usage':
would rather: past tense with present or future meaning
We can use would rather to say that a person would prefer somebody to do something. We use a special structure with a past tense.
would rather + subject + past tense
I'd rather you went home now. Tomorrow's difficult. I’d rather you came next weekend. My wife would rather we d id n ’t see each other any more. ‘Shall I open a window?’ ‘I'd rather you didn’t.’ A present tense or present subjunctive is possible (e.g. I ’d rather he goes / he go home now), but unusual. To talk about past actions, a past perfect tense is possible. I ’d rather you hadn’t done that. However, this kind of idea is usually expressed with I wish (► 632). I wish you hadn't done that. In older English, had rather was used in the same way as would rather. This structure is still found in grammars, but it is not normally used.
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