In between reading the author's catagories and my first reply I've listened to the Friday show.
Going with the pet murder example given during the show I'll explain why I think levels lower than Miniarchist would not be fuctional. At the individual level you can choose to be any or none of these. I approach this as how each classification would work if it was the social order in a given place.
The Pacifist would go through a lot of cats. Their nonviolence encourages violence in this example as the violent members of society would go unchecked.
Self Defense Libertarians would be little better unless the person chose to murder the cat while the SDL'er was home. Once the cat is murdered (a process easily completed before the SDL'er can retrieve a weapon to defend his property - the cat) it seems all all the offender need do is step off the property.
The Free-Market Reparationists would go through a lot of cats. Perhaps even more than the Pacifists and Self Defense Libertarians as they would have means (the reparation) to buy more.
A Minarchist would want to be compensated for the economic value of the cat, if any, and have the person punished for their behavior. I happen to believe the threat of punishment is a deterrent, you may not. A Retributionist would want the person punished as well, but that leads us down the private law path. As I think Ian mentioned the cat may be priceless to you. Under a Reparationist, Self Defense or Pacifist system I - and anyone else who doesn't subscribe those principles - am encouraged to apply my own justice. There's no deterrent against future cat mudering if current cat muderers are not punished. And yes, I have an innate feeling people should be punished for their crimes as well. You can ostracize me all you wish and call me a beast, but if your system allows people to murder my cat I'm not going to much care if the people under that philosophy ostracize me from dawn to dusk. After all, once we're done fighting in the street I'll still have the cat murderer to conduct business with - for won't he too be ostracized?
While the Minarchist government's punishment may not be perfect it is a defense against vigilantism. One might say private law is little more than contracted vigilantism. To give a real life example of why I'm so opposed to this concept of private law consider the Pinkerton men. (what's a post without a wiki link?
http://en.wikipedia.org/wiki/Pinkerton_National_Detective_Agency) If you don't like current police you sure wouldn't have liked the Pinks. Yet that's private law. Oh, but that was a long time ago. Hmm, how about an updated version?
http://mediafilter.org/Images/CAQ/PcopsSRC1.jpg He, or the private company's advertising copy, look any more friendly than government cops?
The Limited-Government Libertarians,
as described in the list, was too open ended for me to choose.
--BEB