Ok, so I agree about the whole idea about privatizing roads; it could potentially work. however, we still have the problem with police and crime. Say I am part of one Police organization, and then the person living next door is part of a different, bigger, PDA. My neighbor comes and rapes and kills my daughter. My PDA goes to his PDA and says "Hey, Jon Doe did something wrong, he needs to be punished". Then they say "well to bad, he's a very valuable costumer". So then your PDA tries attacking the other PDA, but because the rapist/murderer's PDA is larger, yours is defeated. You're now basically stuck with a defeated PDA and a neighbor who just raped and killed your daughter. You say, "I'm going to take law into my own hands". So you go and kill the neighbor. Then the neighbor's PDA comes to your PDA and says, "hey, that guy needs to be shot because he murdered my client". Your PDA, being weaker, is forced to hand you over. You are then shot.
See, it just doesn't work. In the end, Anarchy becomes a "Whoever has the biggest gun has the most power" type of thing.