What question that has to asked about this system of thought (anarcho-capitalism) is if markets run more or less efficiently with the existance and/or interference of government. I've been reading Stiglitz, an opponent of what he refers to as "market fundamentalism;” this is what he says in Globalization and its Discontents:

The [2] is a footnote that states:

Now, I’m not one to even begin discussing the intricacies of the economics above, but it seems to provide an empirical answer to anarcho-capitalist assertions. I understand very little about equilibrium theories and Pareto efficiency, so if someone here understands these “mathematical proofs” of Arrow and Debreu and how they illustrate the idealized nature of the invisible hand, please enlighten me with layman’s terms.

I really want to get a general discussion on the feasibility of an anarchist-capitalist system, theoretically and practically (I’ll have to sit out on a discussion on the economics above).

Theoretically, it seems there is a possible answer to every concern, I’ve noticed. The answers may be of various qualities, but they are hard to prove or disprove because of history. A market of today’s industrialized and technological nature has never existed without some form of government intervention. For this reason, I don’t think a discussion of theory is going to get far, but I encourage it nonetheless.

My main concern is practicality. Ambiguous and I have touched on the issue of application in another thread. He or she admitted that an anarcho-capitalist system would likely require a violent upheaval of the status quo, and that the immediate rise of a newly militarized state is a real potential. As it is, this philosophy is held by a relatively small number of people, and its advocating the destruction of the state is not going to earn the support of many policy-makers. The question of implementation is the first one. The second question is of maintaining the system. I’m not even sure if it is worth bringing up quite just yet, though, since I’m very curious about how the theory would even get past the problem of the state and the immediate rise of a new one. We’ll see where the discussion leads.

__________________
No man is an island...
Each man's death diminishes me,
Because I am involved in Mankind.
And therefore, never send to know
For whom the bell tolls;
It tolls for thee.
—John Donne

It's hard to say why Stiglitz believes this since he doesn't go into much detail other than to reference himself, essentially saying that his assertion is correct because he says it is. While that doesn't necessarily disqualify his statements, neither does it back them up (which is what they would have to do since the burden of proof is on his shoulders).

There are practical limitations to anarcho-capitalism, as it relies heavily on everyone buying into the system. In that respect, it's not unlike other economic systems that people believe would work if only everyone were on board. The most prominent example I can think of are the Indians. All it took to wipe them out was a large nation of people organized under a government. Likewise, if I and four or five of my neighbors were to dissolve our association with the US and create our own "nation" (yes, I understand the practical limitations of this, but since we're having a theoretical discussion just go with me for a minute), we'd stand little chance. While we'd have no problem interacting with people in the US, it's impossible to expect the US would let us remain independent. Force would be used to bring us in line with the rest of the population because we'd be deemed a threat to the security of the US.

Ultimately, the power of government is unmatched. And in a world where power equals control, the only outcome is government. People fear liberty and would rather exchange it for security. There's a certain sense of peace that comes from being protected by a bully when the only cost for that protection is your milk money.

His citation of himself is pretty disappointing, but I haven't been able to get a hold of the article to read and evaluate. I doubt I'd really grasp the concepts discussed anyway. Still, he does point to the Arrow-Debreu model as well, which supposedly provides the math to show under what conditions the invisible hand works perfectly; according to Wikipedia, "[a]s well as stringent restrictions on excess demand functions, the necessary assumptions include perfect rationality of individual complete information about all prices both now and in the future; and the conditions necessary for perfect competition." The same article goes on to state that Frank Hahn defends general equilibrium modeling because "[g]eneral equilibrium models show what the economy would have to be like for an unregulated economy to be Pareto efficient." [General Equilibrium] Stiglitz and Greenwald seem to have just taken the logical step forward and said that, since real economies do not conform to the assumptions of this model, the invisible hand does not work as described in theory.

I think some people to fear the degree of liberty you're advocating, most likely because they do not believe it would work in practice. I'm not sure where I stand on the stability and endurance of the anarcho-capitalist philosophy, but what I fear is the process of establishing such a system. You yourself seem pretty resigned to the existance of government; instead of aiming for such a high ideal, why not take a more reformist approach through the system itself?

__________________
No man is an island...
Each man's death diminishes me,
Because I am involved in Mankind.
And therefore, never send to know
For whom the bell tolls;
It tolls for thee.
—John Donne