Justice in a Natural Order

Recently I found myself in a lively debate over how criminal justice systems would work in a Natural Order (stateless) Society. I had to gracefully accept defeat as I was not fully read in this particular area. After a quick email to Professor Hoppe, I found a wealth of information on this topic. I have linked a few of the most profound arguments below.

Order Without Law: Where Will Anarchists Keep the Madmen?
By John D. Sneed
Journal of Libertarian Studies, Vol. 1. No. 2, pp. 117-124.

Punishment and Proportionality: the Estoppel Approach
By N. Stephan Kinsella
Journal of Libertarian Studies, Vol. 12. No. 1, pp. 51-73.

Inalienability and Punishment: A Reply to George Smith
By N. Stephan Kinsella
Journal of Libertarian Studies, Vol. 14. No. 1, pp. 79-93.

The Private Production of Defense
By Hans-Hermann Hoppe
Essays in Political Economy from the Ludwig von Mises Institute

Natural Order, State, and Looting
By Hans-Hermann Hoppe
LewRockwell.com

Now I know this is weighty stuff, but if you commit yourself to read through an article or two, I'd really like to hear your thoughts. Please comment.