The problem is, what is a democratic global government? Larger states dominate smaller states in democratic governments all over the world simply because of numbers of votes. Having yet another layer of elections over it doesn't really make much of a difference.
> Larger states dominate smaller states in democratic governments all over the world simply because of numbers of votes.
At what governance level would this be acceptable for you? The existence of political minorities is invitable. The question is where do you draw the line: street, block, postal code, city, metro, region, state, or nation? When is it ok to dominate others because they got less votes? The same issue is reflected in red states grabbing power from blue cities, with the implication that the state-level domination is A-OK.
We're not going to structure a global government, such a thing is never going to exist and we're never going to have to worry about it existing. Fortunately.