Turning a Negative into a Positive
I do believe there are some psychological theories which are important to remember when dealing with these situations. I suppose this would relate the closest to personality based psychology, with the study of the differences and likenesses of everyone's personalities. You can also tie in some social psychology as well.
Are people talking in a negative way to garner attention?
Are the people simply venting and need an outlet?
Is the reaction proactive or reactive?
There are variables to the persuasion as well. Think, who said what to who and how.
You have Communicators who uses credibility, expertise and trustworthiness to persuade. You have the Message using reason, emotion (e.g. anger or fear), arguments, and other types of informational content. The Audience, what is the message targeting? And the Channel or how it's being presented, via print, speech, etc.
If you can use some of those theories to help dissect the problem and in turn come up with a solution, it may turn a negative persona into a positive one.
How do you approach someone who is hostile, well simply put you can't meet them with hostility. You'd need to approach them with some sort of understanding, almost like a hostage negotiator would.
Respect what people have to say. Even if they can only voice concerns with negativity. If they really don't care they probably would look to discuss their concerns somewhere else. If you approach the person with respect, the chances are this will be reciprocated. Sometimes you have to give a little respect to get some respect.
Listen to what has to be said. Don't look to talk over or point out the bad things, try to listen and understand how something is affecting that person. How is it making them feel? Sometimes regurgitating what's being said shows signs that you are listening. Try using what they have said in a response back to them.
Be helpful. If someone is negative because they are frustrated that they can't find the answers they are looking for we should try to help them find the answers. Making sure that their voice is heard and providing the help that we can, helps soothe dejected feelings.
People have names. Try to use their name when applicable. Online especially when you can easily fade into a crowd, having a face and a name can make a difference in diffusing a bad situation. You won't be on a first name basis with everyone but if you say "Hey X, I was wondering why you were doing X" it comes across as being much more personable than "I was wondering why you were doing X". Typically you'll have a greater chance of having a positive reaction after making such an effort. You shouldn't use someone's name to call them out in a situation however; this will only drive a wedge between you and that person. It can also lead to some very jaded feelings.
Follow through on what you say. This is simple but time and time again we fail to deliver what we promise. Following through on what we say can only build trust in a community. It's especially true when the negativity comes from distrust. No, we're not politicians, but a promise is a promise, and we should respect players enough to follow through on our promises.
Exude calm and positive solutions. If we stoop to a level where we don't show that we're calm and positive it will only feed the fire. In a virtual world where you can easily misread something, having clear and concise answers that are worded appropriately is imperative. Positivity counts too, try talking about a positive instead of a negative. Think of it as what you can do as opposed to what you can't do.