"I will try to express myself in some mode of life or art as freely as I can and as wholly as I can, using for my defense the only arms I allow myself to use -- silence, exile, and cunning." -- James Joyce
The Mexican drug cartels are a really interesting phenomenon since they have the power to rival Mexico's security forces. When I look at these things, though, I try to avoid using the labels "public" or "private", since those only make sense in a larger context. So, I'd probably call them for-profit security organizations or something like that.
A friend of mine used to live in El Salvador. People in his neighborhood kept getting robbed, so they pooled their resources to hire a couple of security guys to patrol the area... only to have the security guys rob them all at knife point. There's a lesson here somewhere.
One of my friends bought food from a privately owned restaurant, and he got sick.There's a lesson here somewhere.
There sure is Bob: both states and private enterprises are populated by flawed human beings, and both screw up.
I'm beginning to suspect that labeling might have a distorting effect. For example, it seems perfectly fine to call the Pinkertons a "private security firm", but to apply that label to a clan in Somalia or a drug cartel seems off. The "private" in the phrase "private security firm" only makes sense if there is a "public" with which to contrast it against. Is this something along the lines of what you mean by rationalism?