SUBJUNCTIVE WOULD RATHER/WOULD PREFER
Would rather/sooner are followed by infinitive without to
when the subject of would rather/sooner is the same as the subject of the following action:
A : Would you like to start today?
B: I would rather /sooner wait till tomorrow.
prefer can be used similarly with the full infinitive/ infinitive
A: Would you like to start today?
B : I would prefer to wait till tomorrow.
If however, the next action has another subject,
Would rather/sooner requires a past tense.
A: Shall I give you a cheque for Rp 100 000?
B: I’d rather you gave me Rp 100 000 in notes.
A: Would you like him to paint the door green?
B: I’d rather he painted it blue.