I came across Prove that $\phi(x) = 2x^2$ : $\phi[-1,1] \to [0,1]$ has two fixed points from a new user. It's a question with several thoughts/attempts at methods of solving it and it had -2 votes when I came to it. I thought this was the kind of thing we'd want to encourage new people to do, not discourage...unless perhaps the downvotes came from the pre-LateX formatting? Even so, for a new user that doesn't seem like a good idea to me. Or am I missing something?
Questions that have clear research efforts do occasionally get downvotes. I don't have much explanation for this other than the down-voters either did it on accident (as was suggested in the comments), or they just didn't like the question.
I have some personal experience with this. Perhaps it is the style of questions which I ask, but nearly every question I ask gets a certain amount of downvotes, regardless of how much effort I show. For example this post received a downvote, even though I clearly showed an effort to provide context and I did what I could to solve the problem. I figure that those who downvote questions like that decide that these questions are not useful or interesting.
If that's the case, I guess that every given question has a certain chance of getting downvotes based on the fact that a certain number of people are bound not to think it is interesting or useful. As it is, I don't see it as much of a problem for experienced users like myself, but it could be a deterrent to newer users.
If you hover your cursor over the downvote button, it says "This question does not show any research effort; it is unclear or not useful." Perhaps, if the rather subjective evaluation "not useful" were replaced with something less subjective it would fix this problem.
If the downvotes are unintentional, as in the case that @ParamanandSingh commented about, we might benefit from a change in the layout of the mobile version of the site. Of course that depends on whether or not these accidental downvotes are deemed a big enough problem by the powers that be.