I recently cast an upvote to reverse a downvote that had been given to this question.
Subsequently, another user and I debated whether I should have upvoted the question. Our back and forth comments were each posted following the question itself.
While you can read the original comments that the other user and I each posted following the question, in an effort to make this answer self-contained, I will repeat my thinking here.
Since my reasons for making the upvote are somewhat long-winded, I think it best to describe them in this answer, rather than in the comments.
First of all, I think that the point made in the (already existing) answer of Kaveh, to this posted meta-question, is very well taken. That is, I think that the effect on the poster's rep should be consistent with [1 person 1 vote], and the existing [$(-2)$ - downvote ::: $(+10)$ - upvote] mechanism is unfair.
I also think that it is fair to point out that I did not originally upvote this question. Instead, once I saw that the question had been downvoted, I reacted to the downvote.
This is one side of the ledger.
From my perspective, the other side of the ledger is represented by points made in the already existing answer of Phira, to this posted meta-question.
For reasons explained in the next section of this answer, my opinion is that the question does not deserve a $(-1)$ score. I distinguish this from the conclusion that the question deserves a $(+1)$ score.
Further, I think that Phira hit the nail on the head, when he focused on the psychological effect of a downvote. I regard that effect as being the most important consideration in this situation.
Therefore, I feel that it is important to upvote in such a situation, as long as I also include a comment that clearly explains my thinking.
From my perspective, the real value to the OP in this situation is the combination of my upvote combined with my comment clearly explaining my thinking.
The remainder of this posting focuses on the specific question that I downvoted. I am unsure how pertinent one specific example is, to the generic issue of upvoting to reverse a downvote. However, I don't see the harm in focusing on the specific question, and explaining my evaluation of this question.
The OP started with an extremely worn-out question:
(In effect) prove that $\forall n \in \Bbb{Z}, ~n^2~$ is not congruent to $(2) \pmod{3}$.
Obviously, the most common approach to this question is to first focus on the manual consideration of $a^2$, for $a \in \{0,1,2\}.$ Then, you compare the congruence, (mod $3$) of $a^2$ with $(a +3k)^2.$
The OP took an unusual approach, that I have never seen before, that I consider creative and potentially workable.
That $a^2 \equiv 2\pmod{3} \implies (a+1)(a-1) \equiv 1\mod{3}.$
Then, in trying to implement this approach, the OP confused the conclusion that (for example) $(a+1)$ is not a multiple of $(3)$ with the conclusion that $(a+1)$ is not a multiple of $(2)$.
Then, the OP showed work, in attempting to prove the desired result, based on the OP's erroneous intermediate conclusion.
I don't see how an analytical error in the work shown justifies downvoting the question. I also don't see how the use of a workable but very non-standard attack on the problem justifies downvoting the question.
Further, besides the OP's creativity, I was positively influenced by the fact that he showed work and then (in effect) asked : is this work valid?
I do not understand what frame of reference leads one to downvote such a mathSE question.
So, what it comes down to is:
I think that the combination of the OP's creativity and work shown deserves to not be downvoted. I stated that in the comments, following the question.