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I have seen several times answers being wrong or incomplete or much poorer than others, but due to the fact that they were answered early or accepted as the best answer, they keep receiving upvotes and stay on top.

Of course this can be a subjective judgment and in theory upvotes are accurate, but some cases deserve at least a debate.

Is there anything that can be done ?

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    $\begingroup$ This is discussed routinely, most recently here. Voting is subjective and arbitrary quite frequently. $\endgroup$ – user61527 Jul 3 '14 at 7:37
  • $\begingroup$ What can you do when you feel that the upvoted answer is plain wrong ? $\endgroup$ – Yves Daoust Jul 3 '14 at 7:40
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    $\begingroup$ Leave a comment, and then downvote as needed. Most people are pretty receptive to this. $\endgroup$ – user61527 Jul 3 '14 at 7:41
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    $\begingroup$ The comment will have little chance of being read, for the same reason, I'm afraid. $\endgroup$ – Yves Daoust Jul 3 '14 at 7:43
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    $\begingroup$ It'll almost certainly be read by the author (and I think most at least skim over the comments). $\endgroup$ – user61527 Jul 3 '14 at 7:43
  • $\begingroup$ Let me suggest to revise the belief that "in theory upvotes are accurate" if "accurate" means "corresponding to mathematical correctness of the answer". :-) $\endgroup$ – Did Jul 3 '14 at 8:51
  • $\begingroup$ @Did: didn't I say "in theory" ? :) $\endgroup$ – Yves Daoust Jul 3 '14 at 9:52
  • $\begingroup$ You can probably find several discussion related to incorrect answers posted on the site; for example: meta.math.stackexchange.com/questions/10160/… $\endgroup$ – Martin Sleziak Jul 3 '14 at 11:54
  • $\begingroup$ The "accepted" answer isn't still receiving upvotes from the looks of it, but this makes for an example of the phenomenon of this question math.stackexchange.com/questions/256017/… $\endgroup$ – Doug Spoonwood Jul 9 '14 at 2:29
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    $\begingroup$ One of the things you can do, when you see a wrong answer getting too many upvotes (acceptance even) in comparison to a correct answer is to draw attention to it by giving a bounty. I don't necessarily recommend that you start doing this yet, for you should still collect more rep to gain all the privileges. OTOH, I have rep to burn :-/ $\endgroup$ – Jyrki Lahtonen Jul 9 '14 at 8:48
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    $\begingroup$ I would bring a list of example here to meta for discussion. The increased attention and traffic will probably result in additional votes (or even better answers). Especially in clear cases this should efficiently improve the whole situation. $\endgroup$ – Trilarion Jul 11 '14 at 11:41
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From the Help Center:

Reputation is a rough measurement of how much the community trusts you ...

This has been the definition of reputation for as long as I can remember.

People upvote substandard answers. People downvote because they're having a bad day. It happens.

Also, your reputation, plus 99 cents, will get you a mediocre cup of coffee.

If you help someone, or if someone else helped you, you've won.

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    $\begingroup$ It used to get a bit more than that, e.g., a mug in which to hold that 99-cent coffee. I haven't heard anything about this recently, perhaps the practice was discontinued. (?) Although top MathOveflow users were promised MO swag recently. $\endgroup$ – user147263 Jul 6 '14 at 23:30
  • $\begingroup$ What worries me is precisely the inability to help others when you see an inappropriate answer that is "self-feeding". Neither downvotes nor comments do work. There's probably no way, you can't at the same time impose your own opinion and respect democracy. $\endgroup$ – Yves Daoust Jul 9 '14 at 7:42
  • $\begingroup$ I got a plastic/rubber piggy bank, stickers, and a T-shirt from money.se. :) $\endgroup$ – John Jul 10 '14 at 16:29
  • $\begingroup$ I do agree mostly that you, as one person, can't do anything by yourself to "right a wrong." That's by design. But, if you do downvote (and explain) or comment on a better answer (and explain) then you're leaving a trail for other people to see what you see. It has to have more effect than doing nothing. $\endgroup$ – John Jul 10 '14 at 16:35
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I would say that voting is a rough measure of (perceived) helpfulness.

All other things being equal, a "fast" answer is considered more helpful than a "slow" or "delayed" answer. Unfortunately that is true (on this site) even if the slower, longer more thoughtful answer is objectively better than the fast answer. To paraphrase General George Patton, a mediocre attack today is more useful than a brilliant attack a week from today."

I, (and probably others), upvote answers based on their usefulness to me. I can't judge the best answer (in math, anyway) from its value to experts. The best proxy is its value to me. So a simple answer that seems to "make sense" could possibly be more "helpful" than a long, detailed, "airtight" answer.

I do give a lot more thought to downvoting. I won't downvote on "mere suspicion" but only when I am sure that something is (seriously) wrong.

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    $\begingroup$ I highly doubt that answer speed plays a large role in the general assessment of helpfulness. Rather, I suspect that the primary reason that later answers receive fewer votes than earlier ones is simply that they generally receive fewer views, because many readers don't revisit threads after their initial view (esp. if they browse questions via the "new" vs. "active" tab). Also quicker answers tend to be shorter and less deep, so are quicker to assess. $\endgroup$ – Gone Jul 8 '14 at 19:18
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There's just no voting system that will always deliver the right results. Of course, after the 2000 U.S. presidential election, plenty of cranks thought they had come up with the silver bullet, and several normal people suggesting Americans should ditch the Electoral College.

At least on this website, the moderators seem fairly hands-on, they can take steps to address the more egregious cases. Though I'm sure they also get criticized, sometimes for doing too much, sometimes for not doing enough. There's just no perfect system.

As for what you can do, here are my suggestions:

  • If an upvoted answer is a little incomplete or it's wrong on some minor technicality or it has a little typo and you know where it went wrong: just fix it! I edited one answer where the editor had left out one instance of a variable in a formula with several instances of the same variable, and another one where several people had misunderstood an esoteric subtlety. No big deal.
  • If an upvoted answer is just plain wrong and the only way to fix it would be to completely rewrite it, well, then that's what downvotes are for, so downvote and leave a comment starting off like "I'm downvoting because..." And, if worse, the asker has accepted it, then you have to post your own answer. The asker can then unaccept the bad answer and accept yours. I can't remember if I've ever unaccepted an answer, but I know I can do it if I need to.
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    $\begingroup$ The moderators apparently have very little knowledge of voting; they are only notified of suspicious voting patterns, and everything else is left up to SE. They do not intervene in cases of technically incorrect answers being posted or accepted. $\endgroup$ – user61527 Jul 7 '14 at 6:41
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    $\begingroup$ Agree with the general sentiment of this answer. But I also agree with T.Bongers. It is not the moderators' job to arbitrate disputes of mathematical correctness. That's our job. Commenting and voting (not forgetting about the possibility of posting a correct answer) are the tools given to us. $\endgroup$ – Jyrki Lahtonen Jul 7 '14 at 7:22

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