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I totally agree that the key feature of a high level academic forum is the audience choice, which is by all means given in terms of up and down votes. Nevertheless, I would like to point out some little misbehaviours thereof and suggest if, at least for some sections, downvotes could be removed at all.

I am a theoretical physicist and, although having always been a big fan of this platform, I have only joined it actively lately. The reason is that most of my colleagues and my community left the forum after a while due to the ridiculous way people downvote correct proofs in mathematics without even giving (possible) counterexamples. I regret I have to say this has been happening to me as well and is giving me good thoughts to drop the forum as they did, without wasting any more time if people do not even read the solutions.

If you find the answer useful then one may upvote. If not, one can just not upvote it, leaving it to zero score. Downvoting an answer without counterproofs, besides questioning someone else's effort and time, also evens out and discards all the ones who had previously upvoted the same answer. Especially in technical areas (physics, mathematics, chemistry and so on) a proof is either true or false and I would suggest that in those sections downvotes, if still useful at all, should be allowed only after proving the related answer to be explicitly wrong, giving a counterexample or meaningfully expanding it. Otherwise, no downvote should be allowed.

I have seen that many other users pointed out, along similar lines, the same feeling. What's the state of the art about this issue here?

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This is certainly an interesting perspective. I'll approach it in a new way, from your angle.

On Physics Stack Exchange, one of the science sites I'm most active on, I see a lot of crap. I don't mean to say that most of the material there is wrong - the vast majority is good or better. But I see many instances of people posting wrong answers. As an example, someone might ask

Why is some dark matter distributed in a halo around a galaxy?

An answer of the type I'm talking about might read

Well dark energy permeates the universe and there are currents that run along the magnetic field lines of the galaxy turning it into a shape

This is wrong on many levels, i.e. almost everything. In theory, this is not an answer that is delete-able. It is wrong, but wrong answers are not deleted. (Well, some are.) If the answer was

Well dark energy makes the stars move like they do!!!

then it would be delete-able, because it is not an answer. Downvotes help here because they push answers like these to the bottom.

A response to this might be, "Well, why not just leave it at zero?" A valid point. But how does one distinguish a post like this with another unhelpful post - one that might attempt to answer the question, and is relevant, but isn't really upvote-worth? Leaving both of them at zero does an injustice to this other answer. Thus, the ability to downvote.

This is just some rationale for how downvoting can be helpful on science sites; you can extrapolate it to Mathematics and Math Overflow.

You agree with this, I take it, from

downvotes, if still useful at all, should be allowed only after proving the related answer to be explicitly wrong

The problem, though is that it's not really possible to remove the downvoting feature from only some questions. Besides, how would you determine which ones those were? On any proof question, someone could still post a crappy answer like the one I gave as an example. Are you saying that downvotes shouldn't be allowed on something like that?

I think that this provides a counterexample.

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    I totally agree with you. What I suggest, which is also the way other platforms work, is to distinguish between "scores" and "votes". Users can up and down vote whatever and however they want, but scores are assigned only after a certain threshold has been passed. For example: downvotes are free but do not get displayed (in order to avoid influencing the next users) and scores of -1 are assigned only after N different downvotes from different users, which means that if several people mark my answer as wrong, then it must most likely be wrong indeed. Likewise for the up vote.
    – gented
    Commented Jun 27, 2015 at 16:19

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