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Reputation becomes important in pseudo-anonymous and de-anonymised sites. This often leads to popular individuals being able to take control of a discussion. Anonymous posting prevents one or two individuals from controlling discussion and acceptable viewpoints by sheer force of their reputations.
Anonymous posting lets people freely share ideas without threat of recpercussion.
Anonymous posting can allow the idea to stand on it's own, away from the name of the person.
Enforcing real name only policies could be akin to a form of censorship, limiting the freedom of users to post as they want.
Allowing anonymous posting facilitates trolling, which derails useful discussion.
Associating peoples names with their comments online promotes intellectual honesty, forcing people to think through what they write.
They must have the courage to let their name stand by what they post.
Many online communites that have mainly anonymous posters are dogged by trolls, name calling and low quality discussion.
Posters may have ulterior motives for suggesting a topic or controversial viewpoint that does not add to the discussion. An example of this is marketers manufacturing angry discussions over their products to lure in regular users and spread awareness of the product.
Anonymous posting makes it easier to abuse people.
The abuse can have negative impacts on individuals and social networks.