There is a pretty large divide among those whom consider themselves anarchists today. Ever since my conversion (if you really want to call it that) I've been made painfully aware that there are as many subsets of anarchist thought as there are non-anarchist schools of political thought. But there does seem to be a single division for which all self-proclaimed anarchists seem to fall on one side or the other. The schism would be between two general groups who would be roughly labeled as "Leftist-Anarchists" and "Anarcho-Capitalists." Although these groups share a general distrust of almost all of the current incarnations of government, they often seem like they are worlds apart. It's not uncommon to see opposed anarchists, engaging in a pedantic quibble about who the "real" anarchists are.
Leftist-anarchists are mostly united in their opposition of organizational hierarchy...of every kind. A Leftist-anarchist generally believes in a sense of equality associated with hierarchy. They do not believe that one person should hold dominion over another. So they believe that government is invalid because of the obvious hierarchical implications. But they also believe that most business arrangements are also invalid, as an employer or share-holder is situated above the employee. They generally believe in a more "Georgist" sense of commerce and social interaction in which labor, land, and wealth is owned and controlled directly by the collective of those who provide labor.
Anarcho-capitalists also believe in the invalidity of government but are not opposed to free-market operations. Anarcho-capitalists are rooted in the Lockean principles of Natural Law and the classically liberal notions of personal liberty and spontaneous order. I would classify my socio-political views as falling within this latter group.
I think the axiomatic division between the two groups lies somewhere in the idea of private property. Anarcho-capitalists tend to have a strict idea of property from which all liberty emanates. You are "free" to do as you wish with your body because you own it. Just as you are free to do what you wish with your property because you own it. Leftist-anarchists take issue with the idea of private property because it allows for hierarchy. For instance, if I own an apple tree and you want to eat apples, I can offer to let you take some apples for an hour's work. In the eyes of the Leftist-anarchist, this would be unjust, as my owning of the apple tree places me in a position over you.
I always found this view to not only be antithetical to the idea of liberty, but to be paradoxical in some ways. The initial issue with this mindset is the notion that withholding my labor or the product thereof (property) from you is somehow a positive violation of your rights as an individual. Viewing it as such, owning ANYTHING that someone else wants and/or needs yet doesn't have would constitute something "evil." Now, it is certainly true that being a human being in and of itself endows us with certain biological needs and wants which we cannot mitigate to a large degree. We all have a general need for food, water, clothes, shelter, medicine, and so on. But it isn't clear (in an ethical sense) that this demands positive obligation from each one of us to provide our labor or the products thereof to everyone else.
If I purchase a plot of land, plant an apple tree, and spend years watering and fertilizing it, trimming it when need be, until it begins to yield apples, how does this act in and of itself pose a violation of another's rights? On the contrary, if I own myself and my labor, then wouldn't a supposed forced obligation of that labor to the ends of another person actually pose a violation of my rights? The confusion stems from a sense of group rights as opposed to individual rights. Leftist-anarchists believe in the rights of the collective "we" to control as an aggregate will. But of course, the irony is that this runs roughshod over the idea of self-ownership and personal liberty if we can only agree that I own my labor and the product thereof. If I, as an individual, wish to apply my labor or use the product thereof in a way contrary to the will of the collective, then I am in the wrong in their view.
But this brings out a more subtle point that I believe might be lost in the argument. Although Leftist-anarchists do not believe in hierarchy by name, they seem blatantly unaware that they do promote hierarchy in a very real way. But what's obfuscating that reality is the complacence they find in "equality." It's true, in most Leftist-anarchist systems no one person is above another per se, but, in contrast, ALL PEOPLE are above the individual. If an individual decides to do something that is not liked by the majority of such a society, they will find out quickly that their is a very real hierarchy in which the rest of the collective has subjugated their individual will.
However, with Anarcho-capitalists, said person would be able to do whatever he wishes so long as he does not violate anyone else's property. And while our free-market devotion beckons the retort of "Hierarchy!" from our political brethren, it's important to notice that the idea of vertical organization in and of itself denotes nothing good or evil in the minds of Anarcho-capitalists. What matters is force and the violation of the individual. For instance, Anarcho-capitalists are vehemently against the forced hierarchy of government structures, which demand obedience from the individual without reference to choice. However, if an individual volunteers to offer his services to another person in exchange for other goods or services, it's not clear to the Anarcho-capitalist why such an establishment of "hierarchy" in the eyes of Leftist-anarchists would be considered evil. Some Leftist-anarchists will volley with lines like "Capitalism is the freedom to choose your own masters!" and yet without reference to individual freedom, how do such statements hold up? They seem to forget that even if you wished to view the voluntary trade of goods and services as a master-slave relationship, you still will not have made a reference to volition. An individual in an Anarcho-capitalist society can just as well withhold their labor and property from others. Interestingly, that implication isn't exactly as clear regarding most Leftist-anarchist systems.
I realize that this is speaking to a pretty narrow bandwidth of people. But I thought the dichotomy between the two is interesting nonetheless. I do find many Leftist-anarchist views more consistent than those of most mainstream views, but I admittedly find some of their arguments frustrating. Their logic can be quite convincing sometimes. But the implications of their views and the ambiguous and contradicting nature of their sense of liberty prove to be baffling more often than not. What is probably most amusing to me is the fact that under an Anarcho-capitalist system, Leftist-anarchists would be more that free to aggregate and set up such a society (or many of them) whereas under a Leftist-anarchist society, the Anarcho-capitalist vision of natural rights and liberty could not be achieved or practiced. In fact, it seems like the ONLY system in which panarchy could truly exist would be under some type of Anarcho-capitalist system, or at least a congruent system. It's kind of amazing that the term "liberal" has become associated with views that have little to do with freedom or the tolerance thereof at this point. If it still means freedom to any degree it only means it in the sense that the individual has the "freedom" to comply.