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My answer to this question this site has gained several upvotes and downvotes by now. That's a fresh situation for me since, generally my answer received solely upvotes or downvotes, but not both. As to this answer, I checked it carefully but found no mistakes, so I just don't understand what's the reason of these downvotings. Therefore, I'm considering to make a flag to ask the moderator for investigating the downvotings, giving explanations if there is any or cancelling the downvotings if they lack reasons. Is this an appropriate act?

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    $\begingroup$ If you get one post downvoted, then probably not. If you've got a stream of downvotes that weren't reversed automatically (suppose two downvotes a day for a few days), then it might be reasonable to flag and ask to investigate. Just one post got downvoted by three users? Nothing for the moderators to find out there. $\endgroup$ – Asaf Karagila May 21 '15 at 7:19
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    $\begingroup$ @AsafKaragila Thanks for your answer. Then what shall I do to know the reason of this downvoting? I really don't want to see any errors existing in my answer, but i just couldn't find them by myself. Thank you in advance. $\endgroup$ – Censi LI May 21 '15 at 8:11
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    $\begingroup$ No idea. Think about it for a few days, and move on. Perhaps with the meta-post here, someone will come along and speculate as to what might be the reason for these votes. $\endgroup$ – Asaf Karagila May 21 '15 at 8:14
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    $\begingroup$ @AsafKaragila Got it. Thank you very much. $\endgroup$ – Censi LI May 21 '15 at 8:17
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Downvotes and upvotes are not solely used to judge the correctness of an answer. Indeed, the tooltips for these arrows say

This answer is useful

and

This answer is not useful

respectively (emphasis mine). That different users could judge the same answer to be of different utility is actually not surprising. It is certainly not something that requires moderator attention. We have no way of determining which users downvoted or upvoted that particular answer, and even if we could determine this we have no way to force those users to divulge their reasons. (We're also not mind-readers, but that should go without mention.)

Furthermore, the invalidation of votes is only done if there is pretty strong evidence that the votes were made based on something other than the (necessarily subjective) merit of the individual post, usually in the form of targeted voting of the posts of one account by another. Outside of sockpuppetry, I don't think I've ever heard of the invalidation of multiple votes for the same post (which must come from different accounts).

What to do? Pretty much what you've done so far. Look over your post to see if there is anything to improve. When you are happy with what you've submitted, move on. As Jesus once said,

There's no pleasing some people.

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For the sake of a brief official answer: no. Please don't do it.

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It's not a big deal, but I for one would like to know why a particular answer has been downvoted. It would be helpful to know if the math is flat out wrong or the post is not clear. I have seen downvoted answers that seem clear and correct, and have had an answer of my own to a very simple problem downvoted. One wonders why.

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    $\begingroup$ I can see this, but having mods investigate won't help unearthing the ultimate motive. People might not even know themselves. Tough as it may be, moving along and pretending it didn't happen is usually the way to go (after you've thoroughly validated your answer of course, both objectively and from a "helpful post" perspective). $\endgroup$ – Lord_Farin May 24 '15 at 22:27

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