I want to add my recent experiences with downvotes here, instead of starting a new thread on the same subject. It may also help to answer this question.
Event 1:
bound on recursive series
When I first looked at this question, there were two answers. A short answer by WimC which gave (and still gives at this moment) a correct expression that is undefined for $\beta=1$, but the limit interpretation is correct for this value as well.
And a second answer by Brian M. Scott that was wrong.
Both answers had 0 votes. So, I voted up the correct answer and voted down the wrong answer to indicate to the OP which expression was correct.
Brian complained in a comment about the downvote and implicitly about the lack of comment accompanying the downvote.
Now, I know the typical quality of Brian's answers and I had no doubt that there was some minor arithmetical error, but it isn't my responsibility to find Brian's boring arithmetical error. The correct expression was already given in the other answer and it was trivial to see that Brian's couldn't be right without checking his calculations.
A downvote is not a value judgment on the poster. And no, I don't feel obligated to explain the downvote of a wrong answer. It is much more work to correct a post than to see that it is wrong, and it should still be marked as wrong if I don't want to spend the time looking for an error for some reason.
Event 2: An answer of mine to a question about the number of digits of $2^{100}$ using a particular hint cited in the OP. I cannot find the question now because my answer has been deleted.
Yesterday, I posted a wrong answer to the question. Someone downvoted it, and someone else said that I don't deserve to get a downvote for a simple typo.
Well, I agree that I don't deserve downvotes, but my answer certainly did.
The fact that it just got one downvote was detrimental because the total number of votes remained positive and the OP accepted the wrong answer.
I think that is very bad to regard downvotes as downvotes of the poster.