It's hard to think of a better alternative than democracy for keeping the citizenry reasonably happy. When you give the people what they've (collectively) asked for, there's little room for them to dispute the process of selecting a government. That of course assumes a true democracy where all votes contribute equally.

Also, I acknowledge politicians are capable of mispresenting their intentions, so to say people get what they ask for is a bit too simplistic. But generally, you should have a pretty good idea of what kind of things (say) Trump vs. Clinton are likely to do if they get elected.

Anarchy would just be primitive chaos. Sure it might be fun for the first couple weeks until someone decides to stick a bullet in you because they don't like your haircut. There has to be some kind of law and order, we can't just let people run amok.