Anonymity creates an environment full of bullies?
Of course it would change the way people interact with one another. Social and situational settings strongly affect behaviour.

It's funny you see it this way. One can argue that it's exactly the opposite! Like with parliamentary elections, anonymity means that people act based on their own beliefs without being swayed by social pressure.

What's more without anonymity, people may start keeping score, which will further bias the objectivity of the votes.

When it comes to services like Stack Exchange, the general idea is that the various opinions will eventually regress to the mean - so the majority has it. Sure, for this to happen you need quite a lot of votes, but my experience is that usually gross down/up votes are justified.