It would be nice if you would bother to educate yourself as to how private law would not only work very well but much better than the coercive monopoly that is the world's current slew of legal systems.
I highly recommend everyone read the free books, Practical Anarchy and Everyday Anarchy at freedomainradio.com. There are also a multitude of brilliant educational podcasts on various aspects of free market anarchism there. The Mises Institute also has great books on the subject. Maybe check out the works of Hans Herman Hoppe, economics professor and one of Murray Rothbard's intellectual heirs.
I prefer to refer you to these sites where you can get all the detail and refutation of the nonsense that "private law would lead to chaos" that you will need - and the information will be better than any short blurbs about it here - and I won't have spend an hour writing what you can read there in minutes - which may expand to hours once you become fascinated with how obviously workable, moral, productive and harmonious an anarchic society will be.
I have a question for the minarchists who are so hostile to the idea of anarchism. If we ever achieve a Paulian minimal state, would you then seek to prevent the anarchists among us from setting up and using competing private court, protective security systems, dispute resolution services and compel our support of the alternative governmental functions?
If not, then why object to our efforts to educate people as to the potential for a peaceful world of freedom, mutual respect and abundance that anarchism will usher in?
Most people on this site support free markets in all areas but then many balk with respect to police, courts and national defense, and endorse socialism in those crucial areas. Look into anarchistic theory a little more and you may realize it is not impossible - theoretically or practically.
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