[Big Papa Goat]

Armed groups don't take voluntary payments from their clients. Assuming the PDA's are better armed then their clients, (making them as much like armies as anything) their clients will have no choice but to a) pay them b) violently neutralize them, either on their own, or with the help of a new PDA (for those playing the home game, thats what we call a state of war) or c) be robbed by them.

And as for an armed populace, why then the PDA's at all? And what if a serial killer is a paying customer? Couldn't criminals of any kind be paying customers? Wouldn't it be unprofitable for a PDA to prosecute its own customers? Wouldn't criminals neccesarily hire their own PDA's? And without laws (don't go all Hobbes on me here on this point now) wouldn't every competing company have a PDA to look out for its own interests? Ya, it wouldn't really be that profitable, but it would be the rational choice for a given group with its own interests to have its own armed group to look out for those interests. I mean, why would you choose to work under the same rules as people you are in competition with?

At the end of the day, I guess I do want you to get all Hobbes on me, and carefully explain to me the differences between your views and those expressed in the Leviathin.
(As an empirical aside, it may be noted that the development of modern market generally coincided with the development of the modern coercive state)