you cant have power if you run out of money to pay for the guys(mercenaries) that you need for it to be in effect, and that tends to happen when you blitz into pointless wars and find yourself opposed by guerillas.
There are incentives other than money, and some of my 'mercenaries' might be coerced into my service. But really, I'd have all the money I needed (to stay in power) once I would have neutroned/gassed the guerrillas and 'acquired' their property. I could also enslave some of them; I would first gas one large city and then issue an ultimatum for the rest and confiscate their weapons. If even a single man would rebel, I would annihilate the whole city as an example to the rest.
if you start harassing people, people wont want to form school contracts and will send their PDA-s on your ass with you and you go bancrupt.
How would they do that if the territory was controlled totally by me? They have no alternatives; I have banned all other schools, and other services, from my 'turf', so to speak. They can't really vote with their feet either, thanks to my electronically surveilled, thug-guarded "Berlin Wall Mk II" that I have on my borders.
Edit: Sure, it would take some time and effort to carve out this type of totalitarian 'mini-state'. You ofc might argue that it is inherently impossible, because of 'an-cap mentality'. But if it could be created - then there would be little financial incentive for 'lawful' companies to attack it. People would cry wolf if they killed civilians (which would inevitable happen) in the process of liberation, and they might be accused of wanting to exploit the liberated territory themselves (which would most likely be true, since why else would they risk the invasion?). If it were a state comprised of criminals instead of oppressed people, they might even resist invading companies. So these 'rogue' states would remain and would form alliances among themselves. Over time, they would swallow most of the 'lawful' territories (assuming those existed in the first place), since they could use force unscrupulously.
the morals of people living in a completely free society are totally different from totalitarian (ask what u can do for ur country) morals, and turning the former into latter takes decades of softening with first a minimal state, trascending into social democracy, into socialism, into totalitarianism.
We can't really know that for sure since such a society, or more appropriately, mentality, has never actually existed.
so how to convert a free anarchy to a minimal state? If the free market is providing everything people need, i dont think its really possible but perhaps you could demonstrate what incentives they could have to give up their freedom to choose and let someone else choose for them.
If your system worked as advertized, I'm sure it would be
very difficult to get people to abandon it. I am of the opinion, like most others here, that economical and ethical do not coincide nearly often enough for such a society to even begin to form. Basically, the mentality would already need to exist in order for it to develop. Hence the accusations about circular logic etc. Perhaps with mass-indoctrination it could be done.
Edit: I didn't really answer your question. It's not that the people would
want to give up the system. They would be coerced into doing it; without a central body to prevent exploitation, there would be countless ways of doing it, as demonstrated my myself, Princeps and others.
One more issue: there is the problem of cartels and bought courts. It would be a wise investment for several large companies to collude and put enough money together to buy themselves a special law that would allow them to form a cartel or simply to merge together. Then these would merge with other cartels, and so on. Once there are 10 companies in the world and they are all ruthless oppressors, who do you go to in order to vote with your wallet? No new companies could form since that would be forbidden by the laws issued by these immensely powerful mega-corporations. In the end, there would only be one company ruling over the entire world... I'm sure everyone can see the downsides of
that situation. How do you prevent that? Do you suggest, perhaps, that the companies would never get to be powerful enough to affect legislature regarding other companies? I'm not so sure the 'invisible hand' would prevent that. It would be a royal jackpot for a company to be able to outlaw other companies.
