Lord of the Flies wasn't about anarchy. It was about human savagery. Though, what can I expect, schools love to over-analyze books to the point of non-enjoyment.
Regardless, anarchy won't work. Though, look on the bright side, you're tied with communism and ahead of meritocracy, so I guess it's not all that bad. Any system that fundamentally changes human nature will never work, that's what I say.
But, I have to say, I'm somewhat of a sympathist with non-socialist anarchy. It's ideas are good, it's just it's taking small goverment (Which I support) to the extreme, which would result widespread looting, etc. But it's better than meritocracy or aristocracy or absolute monarchy, at least if it worked.