There's one user here (and I don't plan to name names) who asks a lot of questions as they read various aspects of statistical literature (though they often don't say what exact document they're reading; it sometimes seems to be well outside the mainstream), but whose questions often betray a failure to actually read the document they're quoting, a failure to read the responses that they get and so on down the line.
I get the impression that if an idea isn't instantly obvious - even right in the middle of a sentence, the response is "post a question!". In some threads, every response seems to just generate another question, or even two, or three, even when those questions have already been answered (I think in the last day or so I have been asked at least four questions I had already answered in previous responses to the same user in the last day or so). New questions then spin off the responses, with little regard for how easily the answers may be found with google or wikipedia or CV itself (or indeed that someone posting such questions would already have the resources to find out even without any of those).
As such, I sometimes take to downvoting for fairly obvious lack of research. At other times I try to ignore that poster. And sometimes I try to answer (... and am then back reliving when my son was a three year old who would just say "why?" to absolutely everything, without actually listening to any of the answers).
So far it's probably only been about one post in 30 that I have resorted to downvoting (I don't know the fraction for sure, I don't keep track, and I've probably voted at least as many up), but I find myself considering it more often recently.
(This is not a concern about elementary questions; I answer much less sophisticated questions from less knowledgeable users quite happily.)
Clearly the 'ignore' route would be okay -- we're free to choose who we want to answer.
But to what extent is (possibly frequent, given the frequency of posts) downvoting for lack of research okay?
I'm particularly interested in suggestions of criteria to apply or strategies to use, both when deciding how to vote on such posts and when replying (if at all) to the user.
Edit: by way of information - this user has generated over 2000 questions on the SE network in under 4 years, a large majority of them in the last two years. I strongly suspect that they actually face virtually none of these questions as actual problems, and sometimes seem to ask questions as little more than a form of entertainment. (If I saw this on one of the stats groups on reddit, I'd consider some of their behavior as effectively trolling.)
Edit2: To clarify - I am in no way suggesting I would vote down a post because someone with a number of substandard posts has posted something which itself is not substandard -- I think each post should stand on its merits (indeed I wish there were more good posts from this user I could upvote - I'd much prefer to upvote good posts and try to encourage suitable behaviour that way); I mention other posts to point out that if I voted down every post of theirs that I thought merited downvoting on its own (through lack of research), then some days I would be downvoting a significant number of posts.