Anarchy: a political system with no hierarchy, that is, no-one has any greater power than anyone else, and consequently no-one oppresses anyone else.
For some reason, people think this means chaos, confusion, and probably a lot of violence. Nothing could be further from the truth: violence is an extreme example of someone oppressing someone else, of exhibiting their greater power. Chaos and confusion? Maybe, if that can exist without violence and oppression!
Anarchy as thus defined might not work, of course, but that's a different question – and without trying it, it's very hard to know whether it would work or not.
Whether democracy works is another question. It's arguable that democracy has never really been tried, either, but insofar as it has been tried, it doesn't seem to work very well. It certainly seems to produce a lot of that chaos and confusion that people associate with their idea of what anarchy is – and a lot of violence, too.
What democracy certainly doesn't seem to achieve is the avoidance of oppression – but then, that's not what it sets out to achieve. The purpose of democracy is precisely to allow the majority to oppress minorities. It doesn't usually work: what actually happens is that some minority takes control, and oppresses everyone else.
That might well be the actual outcome of whatever system one tries.
So my position isn't that anarchy would work any better than democracy – although it might not work any worse, either – but that it's more of an ideal to strive for than democracy. Democracy is only desirable at all because it's a better approximation to anarchy than dictatorship is.
How might one achieve anarchy? Perhaps that's where the violence comes in? Perhaps, but I very much doubt it. For one thing, I've never believed that the end justifies the means; for another, I don't think it would work. Violence begets violence, not peace and harmony.
Come to that, how might one achieve democracy? I don't think violence can do that, either. Something Bush, Blair, and their cronies might do well to consider.