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Question

If I want to talk about my preference in the past which version is more idiomatic?

1. I would have preferred to do my homework yesterday

2. I would prefer to have done my homework yesterday

Answer 1

Hate, like, love and prefer Verb patterns > Hate, like, love and prefer from English Grammar Today.
We can use hate, like, love and prefer with an -ing form or with a to-infinitive:

I hate to see food being thrown away.

I love going to the cinema.

I prefer listening to the news on radio than watching it on TV.

He prefers not to wear a tie to work.

So, you can say: I prefer to listen etc. I love to go etc. I hate seeing food being thrown away.

This is a rule where you have to memorize the fact these four verbs can go either way.

Cambridge Dictionary for love, hate, prefer, like

PAST PERFECT CONDITIONAL TENSE:

• I would have preferred to do my homework yesterday. OR

• I would have preferred doing my homework yesterday.

• I would have preferred to have done my homework yesterday. [OK]

• I would have preferred doing my homework yesterday. [OK]

to have done is the past infinitive. It is used with another verb that shows a completed action before another past action.

PRESENT CONDITIONAL [often with if] I would prefer to do my homework now.

I preferred doing or to do my homework yesterday. [past tense]

Answer 2

The two statements are both idiomatic, and simply have different meanings:

• 2. I would prefer to have done my homework yesterday

  This statement is expressing a present preference.

• 1. I would have preferred to do my homework yesterday

  This statement is expressing a preference held either before yesterday or sometime yesterday.

In both statements, the modal verb "would" signals that you are describing a counterfactual while the temporal adverb "yesterday" indicates that the counterfactual is an alternate past.

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Reply to the OP's comment

Dropping "would" from Statement 2 diametrically changes its meaning: it now sounds like the student did do their homework yesterday, and are now professing satisfaction with—rather than regret over—their action.

Answer 3

Other alternatives:

1. I wish I’d done my homework yesterday.
   I regret not doing it previously
2. I should've done my homework yesterday.
   It was a better idea to do the homework a day ago
3. a) It would have been better had I done my homework yesterday.
   b) It would've been better if I'd done my homework yesterday.
   3 a) is more formal than 3 b)

The conditional perfect in the main clause, formed by would/should/could/might have+past participle, refers to a condition at a point of time in the past that was different to reality. The if-clause uses Past Perfect

4. a) I'd have preferred doing my homework yesterday.
   b) I'd prefer to have done my homework yesterday

Meanwhile, 4. a) would have + preferred expresses the idea of a choice that was not selected at the time, for whatever reason or circumstance.

Instead, 4. b): would prefer + to have PP expresses a present preference for a past action that could have happened but was not chosen.

All the sentences above are meaningful and grammatical.