These are hardly the only alternatives. In case you haven't noticed, the other people here aren't implicitly contrasting democracy with e.g. monarchy; they're implicitly contrasting it with anarchy (probably anarcho-capitalism).
Again, there's lots of possibilities out there. Personally I like the idea of futarchy, though it's untried. But that's not the point; the point is, there's a lot of degrees of freeom here.