It could be? Being a democracy or using democracy as a tool for decision making doesn’t mean it has to happen through government. If you’ve ever made a decision with a friend group via popular vote, does that make you a government? Or did you exercise authority over your friends when they all agreed popular vote was okay to decide where to eat out? I wager neither

And fyi, you’re thinking of a representative democracy, which is rarely ever truly fair, especially considering the scale it’s supposedly applied to.