When is it proper to vote a question down? I can think of obvious instances in which one should vote a question down, such as if it is the third or fourth homework question somebody has asked in a row without showing any work. But what about if a question is well-intentioned, but demonstrates a fundamental misunderstanding of basic mathematics? While I realize that we want to encourage people to learn by asking, we also don't want to give too many privileges to somebody who lacks basic mathematical knowledge. Should I vote up, not vote, or vote down (especially to counter upvotes)?
4$\begingroup$ A suggestion. One should not downvote a question that is at $-2$ or lower. A standing of $-2$ already gives a very clear message. Any more than that is just piling on, which is illegal in both Canadian and American football. $\endgroup$– André NicolasApr 22, 2012 at 17:57
I don't think the purpose of downvoting is to keep users from having privileges on this website (since, for instance, the penalty to one's reputation is relatively small; besides, to obtain privileges, one needs to be upvoted rather than not to be downvoted). Rather, downvoting is a means of claiming that something is wrong with the question, and to signal the community's disapproval. For instance, I would probably downvote an obviously homework question asked in the imperative form showing no work by the OP, not because I am afraid the same user will someday be closing questions, but because that's not what the site is for.
I don't usually downvote questions asked in good faith simply because of lack of mathematical knowledge demonstrated; this a general math board, and I have no objection to elementary questions.
$\begingroup$ Should we avoid unconstructive downvotes, i.e. those which do not follow any comments on how the question/answer can be improved? $\endgroup$– SBFSep 26, 2011 at 16:19
Well, the tooltip on the vote is the only official guidance; hover your mouse over the voting arrows to read it.
This question is useful and clear [upvote]
This question is unclear or not useful [downvote]
Beyond that, it varies and is up to the conscience of each individual user.
That said, I tend to think of upvotes as a general quality barometer. Upvote questions that are emblematic of, and representative of, what you want your site to be. The questions on the front page, for better or worse, represent your site to the average visitor; vote accordingly.
As far as downvotes, I personally recommend reserving downvotes for strong feelings only. I would not downvote capriciously, or on a whim. Only downvote those questions which you feel strongly represent what you do not want your site to become.