There is actually already one perfectly working anarchy: International Relations. The key is that communism, socialism, anarchy and (yes) democracy tend to lose most of the core ideas as soon as you scale them past 1000. Yet there exist good examples of all systems working on a small scale. However in most of those cases, people are not forced to submit to a system, they are given a choice. If that choice were to exist, most of the above systems would work a lot better.
The type of "anarchy" that some people want does not work because they expect no order at all, which to me is impossible. Anarchy (chaos) encoded in the fractal nature of the universe itself, along with order. Chaos and order work together like a seesaw, slightly drifting from one side to the other. You cannot completely get rid of either of them, doing so would make the universe cease to exist. They are the same thing since both allow each other to work simultaneously.
Take a tree, a perfect example of chaos and order working together. The controlled fractal nature is there, with repeating patterns and self similarity; but chaos is also there, making slight/drastic variations on location/sizes of the twigs/bark/leaves of the tree.