BGH's foray into Anarchy for the betterment of the glorious nation of The Escapist
(I'm going to use vast amounts of political philosophy jargon throughout, but I'll try to explain as I go along)
Anarchists hold a fundamentally positive view of human nature and see the state as a corrupting influence and the state of nature as essentially peaceful. In this respect Anarchism is mutually contradictory with Hobbesian theories. Anarchy can range from the belief that the function of the state should be so limited that it serves merely as a police force, or perhaps even just a judicial system acting as a clarifier of laws (as any Lockean would require), to the more fundamental (and better known) fully anti-statist movement to the degree where all power hierarchies are seen as unjust. Throughout my explanation of anarchy I will attempt to sum up how it 'works', but I must make it clear that I'm very sceptical of anarchist theory and I'm probably a little biased. Added to that is the fact that whilst I've studied political philosophy for a little over a year now I'm still not exactly an anarchy 'specialist'.
The State of Nature
The State of Nature is a 'before civilization' mental exercise in which the philosopher attempts to theorise what life was like before we entered into society in order to see why we are in society today. Different political philosophers have vastly differing theories as to how life was pre-civilisation. One view, formulated by Thomas Hobbes, is that in the state of nature human beings were continuously at war with one another. Because natural resources are scarce and the only way to ensure self-survival is to dominate natural resources people would endlessly commit heinous acts upon one another to ensure that they continued to have access to basic necessities such as food and water. Hobbes envisioned a state of nature in which human life is "nasty, brutish and short". Hobbes believed that the only way that we could escape this fate would be submission to an absolute authority, the most powerful person alive, that could ascertain our safety and access to resources. It is the duty of the absolute ruler to prevent his/her subjects from coming to needless harm and it is the duty of the subjects to follow the leader unconditionally.
Locke came a couple of centuries later and had a far more optimistic view of human nature. Locke believed that humans are essentially good. We each want to uphold the law and ensure that justice is meted out fairly. The problem is that we just don't know what justice is. With no society to set rules there would still be vast amounts of unnecessary bloodshed as everyone would act as an arbiter of an utterly elusive law. Locke believed that society would be formed due to the need for a single ratified code of conduct and designated arbiters. This is a far more individualistic version of Hobbes' theory. We're still forming society due to some form of social contract, but, unlike Hobbes, we're not signing over autonomy to a supreme lord.
Jean Jacques Rousseau came at a similar time and acted as the focal philosopher of the French Revolution. He was a socialist and believed that the human being is essentially communal. Unlike Locke and Hobbes, both of whom are far more individualistic, seeing the human as essentially self-serving, Rousseau paints a picture of a human being whose goals and aspirations can only be understood and actualised as part of a 'general will', the will of the larger entity, society. For Rousseau any individual ruler who's seized control has done so illegitimately, because society shouldn't just be a train to drive a single person's will at the expense of the general will of the populace. Rousseau's philosophy is immensely complex and often contradictory, he at once demands a society which presents the individual will of its members as a single goal and censors which silence those whose views contradict the general will. I won't be assessing his theories here, he's a socialist and we're on about anarchism.
The Relation to Anarchy
Anarchists work on a view of human nature that sees the individual as necessarily capable of handling the day to day actions of a society, interacting with other humans peacefully, without the need for government interaction. The anarchist must have a far more Rousseauan view of the state of nature than Hobbesian, because the anarchist wants to say that the state of nature in in some way better than the state of civilization. Anarchists usually attempt to cite some form of contractarianism as the basis for human interaction, the human ability to form and honour contracts with one another. As such a global economy would still work, as those who need workers would form contracts with a worker and those who need something done would form a contract with others willing to do it. Yet, the anarchist claims that this differs from the society of today because modern society has a system of wage slavery due to the hierarchical power relationship underlying society. The chain of power flows upwards. Whilst it's technically possible for a worker to negotiate his or her contract with his or her employee he or she is not actually realistically capable of doing so, because all of the power lies with the employer. Why? Because all of the money being made by organisations eventually feeds up to the big dog at the top of the hierarchy: the oppressive government. The government seeks to protect those on the bottom of the hierarchy the least, because the government is a self-serving entity. In the state of nature this would not be the case. If someone wanted another person to enter into a contract then they would have to be willing to make the contract fair. A music producer would not be able to provide a musician with a vastly unfair contract because the musician would be unwilling to enter into such a contract. Without the presence of the government to ensure that power relations stayed hierarchical there'd be lateral power relationships, in which, hypothetically, many musicians would gang together to acquire a recording studio in which they'd each have equal share.
All in all anarchism is usually regarded as high idealistic. The reality of the matter is that without the presence of a state the majority of public services would not be met. Doctors and other high skilled, high demand workers would be able to set extortionate contracts which others would have no choice but to accept and, without a government to prevent such an occurrence, society would soon descend into an oligarchy (a system where the very few, in this case those with the essential skills, rule over the many) or a brutal libertarian meritocracy (entirely individualistic state in which the best succeed and the rest fail). Although perhaps I just have too negative a view of human nature.
Hope this helped, feel free to ask for clarification!