I haven't read all the posts in this thread, so please pardon me, if the following is going over old territory.

Here's the short version of the Anarcho-Capitalist idea:

  • Everyone own him/herself. Nobody owns nature, unless they put their own effort into cultivating it into something new (working the land, for example), at which point they become owners of this part of nature.
  • Nobody should agress against anyone else, where agressing means taking control of the property of someone else.
  • You may obtain the property of others only through willful exchange (or as a gift).

This would entail a peaceful society, if everyone behaves according to these rules.

When there is conflict (which necessarily happens, since people are not angelic), they seek judicial service from a third party. This third party rules, and if both adversaries accept the decision, peace is restored. If not, then additional judicial instances may be sought. If, in the end, no agreement can be reached, civilised conditions end, and a settlement is sought in other ways (possibly violent).

Violence is likely to be carried out by professional agencies, on behalf of the combattants - however, they may reject to carry out any such violence, if they can reach agreement, or if an agent deems the case unworthy. In such a case the violence may have to be carried out personally.

Under these conditions, those who are more civilised and generally avoid conflict, and more easily reach agreements in case of disputes, will thrive. And those who are less civilised, generally seek out conflict, and tend to seek settlement through violence, will not thrive.

Obviously, to explain everything fully, and without leaving glaring gaps, will take a lot more than can be done here, and I don't wish to explain all the details. There do, however, exist fine books about this topic. I can recommend seeking out texts by Murray Rothbard; these should be available free of charge (as e-pub etc.) from the Mises Institute.

Hope this helps.