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I'm agnostic about whether questions should be downvoted or not, but I think it's very important that the ability to downvote answers should be retained. Sometimes answers are just wrong or otherwise unhelpful and that should be reflected when answers are ranked by votes; this is important information for people wanting to know the answer to the question but who don't have the expertise to judge whether an answer is correct or not. People should learn not to take votes on answers personally.
Besides, enough people are active that great answers already attract a lot more votes than good answers.
I see where you are coming from Stephen, but at the moment I agree with Qiaochu about downvoting answers. I try myself to remember to see if answers or questions that I downvote are edited and mede better, and then undo my downvote or even upvote. I think people should try to do this, and also leave a comment about why they downvote. One thing that is possibly a topic for another thread is the fact you can't change your vote if the question hasn't been edited for a while. I saw a question the other day, I can't remember which, that I had downvoted at some point. It had been edited and made fine, but I hadn't noticed it at the time. When I saw it, it was maybe 10 days after last edit, and I couldn't change my vote.
The system is mildly geared to encourage positive feedback. It costs rep to downvote something. Admittedly, only 1 point, so one can argue that it should be more.
@Georges: I guess I asked for that!
I agree that downvotes, if they are ever cast, should be accompanied by an explanation and constructive criticism. If this is too difficult an etiquette to enforce then maybe one solution is to remove downvotes. However, I am not convinced that allowing 2 upvotes per user per question is a good idea: like Georges says, "you have absolutely no guarantee that the [up]voter is more competent than the poster," etc. Consider the following scenario: Terence Tao posts some thoughtful but incomplete partial answer to a question in a field in which he is not an expert. A mathematician more of an expert in the field of the question judges his comment as interesting, though incomplete, so votes it up 1. A less experienced mathematician, seeing a long post by Terence Tao, decides that it must contain deep insights and so votes it up 2. (Not that Terence Tao's posts don't contain deep insights! But I hope you see the point I'm trying to make here.)
Re: eliminate downvoting.
Does anyone have the data on downvoting? How big is really the problem with people getting upset because of it? If there is a problem, is the best solution technical (prohibit downvoting) or societal (come to the equilibrium where posts by novice users get edited and improved rather then downvoted)?
Re: two upvotes
There already exists the instrument you call "second upvote": it's called a positive comment ("Hey, that's cool, let's upvote it for clarity and good introduction")
Incidentally, there are a few people in this discussion who I haven't seen before here on meta so they may not be aware of a few things. If this is already known to you all then please forgive me saying it again!
Although MO is run by Anton and his gang, the software underlying it is not under their control. They can do a certain amount (how much is something I'm not sure of) such as installing jsMath, but the core structure is beyond their reach. I think that mucking around with the voting system is one of those things that is beyond their reach.
In that case, as well as discussing it here, it's important to add it as a feature request on the site that the people who write the software use. It's called meta.SE and one of the three discussions that are stuck to the top of the list in this forum has more information about it. In particular, someone who feels strongly about this issue should write a feature request over on meta.SE. Then everyone else who wants it should go and vote for it.
Back on topic, I'd go for the societal solution rather than the technical. I rarely vote something down myself, but I do find it useful as a way of gauging what to look at. Since the default is always to do nothing, the mode here is probably 0 votes. If that's also the mean, then that's a useful statistic. If that's the minimum, then I can't separate "Not worth looking at" from "Nobody's yet understood the question well enough to work out whether it's sensible or not".
If looking for a technical tweak, I would go for the "force commenting if voting down". I do try to comment when I either vote down or vote to close.
It's always tempting to try to constrain bad behaviour by Big Means, but if someone's determined to be nasty then they will be. Perhaps if it were clearer that having questions closed or voted down happens to the best of us, then others wouldn't take it so personally.
(Of course, if it does get personal and someone is systematically voting down other people's posts then that's an abuse of the system and I think that Anton has the Power To Deal With That.)
@Steve: I don't see the point. Surely, users of high reputation can more easily afford to lose some of it.
I think it's important to have downvotes in the system.
A quick glance at several user pages says that the number of downvotes in the system is very small (perhaps 30 times less common than upvotes), so I don't think that people are casting them thoughtlessly. I don't often see a post with a negative score without any comments explaining what's wrong with the post. If the goal is to make MO friendlier, I think eliminating downvotes is an artificial way to do it and probably won't work. If the goal is to distinguish great posts from good posts, I think that already happens because great posts get more upvotes. Adding the option of upvoting a post twice introduces more confusion about how to vote (which people have enough trouble with already), and begs the question, "why not have the option of voting a post up three times so we can distinguish posts that are better than good, but not quite great?"
I saw a question the other day, I can't remember which, that I had downvoted at some point. It had been edited and made fine, but I hadn't noticed it at the time. When I saw it, it was maybe 10 days after last edit, and I couldn't change my vote.
I thought you could change your vote at any time after the post had been edited. I'll look into this.
@Steve: Do you mean for the person voting or the person being voted on?
@hanche: If Steve means for the person being voted on, one could imagine a (highly implausible) scenario whereby a cabal of users downvotes enough responses from a user with 10k+ reputation to get them below 10k reputation, thereby stripping them of access to moderator tools. Again, highly implausible.
@Qiaochu: I assumed Steve meant for the person voting.
You can edit questions and answers alike at 2000 rep.
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