[Casiopea]

Originally Posted by Englishlanguage

Having read, I think The house burnt down would be more common if the person who has set the house on fire is unknown; am I right?

Yes, and no. If the agent is unknown but important, then a passive construct would express that better than an ergative one (Please see my edit in post #4. The house burnt down (past tense) is an ergative construct, and doesn't house a middle voice verb.) If, however, the agent doesn't factor into the meaning at all, then an ergative construct would work better than a passive one. (There's more on this below.)

Originally Posted by Englishlanguage

Can I say that The house was burnt down has the same meaning of The house burnt down?

They're different, but first let's show how they are similar.

Passive, ergative, and middle constructs make the verb's object topic:

Verb's object is topic
Passive: The house is burnt down (by someone).
Ergative: The house burnt down.
Middle: The house burns down.

But ergative and middle constructs change the the verb's transitivity:

Transitive
Passive: The house was burnt down (by someone).

Intransitive
Ergative: The house burnt down.
Middle: The house burns down (as the crowd looks on).

In the second and third examples, the phrasal verbs burnt down (past tense, ergative) and burns down (present tense, middle) are used intransitively, without naming the agent (the doer) of the action. The agent is never present; it never figures into the semantics, "no agent can plausibly be supplied. (Source)." On the other hand, with passive sentences the agent (the doer of the act) is always present, even if it's left unstated. (Note, the symbol * means ungrammatical.)

Passive: The house was burnt down (by...).
Ergative: The house burnt down (*by...)

So, in short, those two sentences are semantically different. Ergative constructs place focus on the description of the event, whereas passive constructs involve a doer, an agent, albeit a "passive"--non-paticipatory--doer, but nonetheless a doer is indeed present and factors into the semantics.

Originally Posted by Englishlanguage

Is there any reason for the above google results?

It's hard to tell. Don't let the numbers fool you! We don't know how many of those hits are nested and/or reduplicated; moreover, the spelling burnt isn't a BrE thing; AmE writers use it as well. Conversely, the same holds true for the spelling burned; Some BrE writers use it.

What I can tell you--spellings aside, and just looking at the number in total--is that ergative burnt/ed down appears to be more common than passive was burnt/ed down. Which is what we expect to find, especially if it's the event, and not the participants, that are in focus.

Does that help?