"Hey, how come Andrew gets to get up? If he gets up, we'll all get up, it'll be anarchic."
You could use either, as with many -y/-ic pairs. The meanng is different, but only in a way that is negligible. Usually when people say things like 'That isn't democracy' it's a figurative usage - 'That isn't [the sort of behaviour that is characteristic of a] democracy', which means 'That isn't democratic'. Same with anarchy/-ic.