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Perhaps it is not an issue in sites like MathOverflow because it is really shameful for a prestigious professor to get involve in such childish games but in Math.Stackexchange it could happen.

Here there are many users who greedily seek for higher reputation thresholds. According to the site policies establishing satellite accounts and voting between them is not allowed and the user will be punished if this behavior is spotted.

But what if this voting irregularities happen between different users as a kind of agreement? A user A upvotes almost every post of another user B. In response the user B votes for almost every post of the user A. Both will get higher reputations and this is not "illegal" because they are different users.

What is the site's policy in such cases?

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    $\begingroup$ Nothing was ever officially confirmed, but there was a series of suspensions recently (involving a lot of high-profile users) along with a lot of votes reversals, and it was suspected that the users in question did engage in what you describe here: a "voting ring" of sorts. (The users in question were pretty much gloating in the public chat about their "system", to be fair...) $\endgroup$ – Najib Idrissi Oct 8 '15 at 7:22
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    $\begingroup$ @NajibIdrissi Is this a voting ring or a voting group? Are voters associative? $\endgroup$ – imallett Oct 17 '15 at 21:50
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    $\begingroup$ Personally I don't see the hype...it's pretty sad if you think you "need" stack exchange votes that much to get on in life. They don't equate to money or anything else that is valuable... $\endgroup$ – fretty Oct 18 '15 at 8:22
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    $\begingroup$ @fretty higher self confidence, power, influence on the site $\endgroup$ – tox123 Oct 21 '15 at 1:51
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It is not allowed to make deals about mutual voting, definitely not explicitly and not even implicitly. This would be considered as a voting-ring. Even to just vote on many of a user's post because you might find the user is a friendly person brings you quickly on very thin ice.

Such behavior can lead quickly to reversal of votes and even to suspensions.

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    $\begingroup$ To be sure, it is fine if you have a friend whose posts you like to read and upvote; just make sure you are actually reading their posts carefully and upvoting them based on their merits, not just because your friend wrote them! $\endgroup$ – Eric Wofsey Oct 7 '15 at 23:38
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    $\begingroup$ Actually, I would even recommend some caution in this situation. It is better to vote on posts as one finds them on the site, rather than to go through some friend's recent activity. In that case I think how this is seen will depend mainly on how much of one's relative activity this voting for a friend is. $\endgroup$ – quid Oct 7 '15 at 23:44
  • $\begingroup$ (+1) Thanks for the answer. It is really nice that I can't find any critical typo in this answer of yours! Maybe because my question is very simple and clear and you didn't have that much trouble to get its point! $\endgroup$ – user277482 Oct 7 '15 at 23:45
  • $\begingroup$ @A.M. While I am glad you are satisfied, you cannot have read my post carefully enough when you did not find a typo there. $\endgroup$ – quid Oct 7 '15 at 23:50
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    $\begingroup$ Could you please provide a link to an official statement by moderators somewhere that they clarified the policy in this situation? $\endgroup$ – user277482 Oct 7 '15 at 23:56
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    $\begingroup$ @A.M. see meta.stackexchange.com/questions/138517/… As you can see it is quite strict; see my reply to Eric that I feel is in line with what is said there. Note that Bill the Lizard while not a moderator at the moment was a highly active and influential SO mod for many years. $\endgroup$ – quid Oct 8 '15 at 0:04
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    $\begingroup$ @quid Is this the first post that you've answered with your [user]name in the title? $\endgroup$ – Benjamin Dickman Oct 8 '15 at 4:41
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    $\begingroup$ @BenjaminDickman At some point somebody complained about me on MO, and I commented. I think they had my name in the title. For more coincidental appearance, I might have forgotten or not noticed. But regarding this title perhaps also ask math.stackexchange.com/users/212220/quidproquo :-) $\endgroup$ – quid Oct 8 '15 at 10:22
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    $\begingroup$ Something that sometimes happens to me is: I find an answer I like, I go and read other answers by the same user. To me, that's a perfectly honest way of learning interesting new things, and it is bound to make me upvote this person's answers a lot. Should I be worried? $\endgroup$ – PseudoNeo Oct 12 '15 at 17:12
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    $\begingroup$ @PseudoNeo I suppose it depends on volume. If you stumble across some answers you like and cast a handful of upvotes, it will not cause any issue. (Also note that even an occasional auto-reversal of serial voting is I think inconsequential.) If you read through a list of 2000 answers at a rate of 20 per day and vote on 10 of them each day not doing much else on the site it likely will result in some questions. Anyway, I do not want to create any paranoia here. Just do not go overboard with concentration of votes even if they seem deserved, and things should be fine. $\endgroup$ – quid Oct 12 '15 at 17:28
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    $\begingroup$ This comment makes so much sense I'm going to create a gazillion of accounts to upvote it ;-) $\endgroup$ – PseudoNeo Oct 12 '15 at 17:29
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I would say certainly not.

However, I have adopted a few practices:

First, whenever someone finds an error in one of my answers, I always upvote their correction. My hope is that this will encourage others to read my answers, since my probability of making an error is definitely non-zero.

Second, if someone posts the only correct answer to a question, I post a comment (to the original question) encouraging the OP to accept it, if they have not done so.

Third, and less relevantly, I enjoy a conversation consisting of a series of comments about answers, despite MSE's occasional suggestions of "why don't you two find a room!"

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