Clayton: Yes Autolykos got it right.
However Smiling Dave also got it right. You are disputing the premises that are common sense to anyone but the most naive idealist of libertarian goodness. The rejection of those premises itself is the pitfall that so many accuse libertarianism of: the assumption of manhood being good. It is regrettable that the obsfuscated system of market production of security provided to cover up the issue never addresses the core problem i presented in the opening post. Neither does Ryan do this as I will demonstrate:
Ryan brings up the point of investment: giving up income now for income later in time. This can be true, however what does happen later in the progress of time? It is assumed that the would-be good PDA makes a speculation over higher income in future by providing retaliatory justice as a trade good at present. This is all correct, it is a solid business plan as it decreases the cost of production of security in the future due to decreasing number of bandits having to cope with.
It has happened in history and in fact is the precondition of formulation of state itself, as well as being the business plan of state’s income insurance. The key about this action however is that if successful, the fundamental premise of my OP does not go away. Though the pda has increased his popularity, made income by exchange, the fact remains that whatever income he can make in the future, will still be higher if he extorts it instead of exchanging for it. You cannot give more money to someone offering to protect you from theft than to the robber robbing you, the paradox of production of security is, as mgmcintyre argued in his thread The failure of Anarcho-Capitalism
Note that it can be argued for directly, ignoring my premises. I assumed opportunity cost of robbing a citizen being lower than that of robbing a bandit for the same income. The other way to argue is to assume that for equal opportunity cost robbing someone results in higher income than them paying you to rob someone else.
Aah yes the appeal to morals. A common response, also from the larger thread i linked to. Let me ask you this, what is the difference between offense and defense? Other than prescriptive morals that a large portion of this forum subscribes to, there is none.
The fact that one happens before the other implies nothing about the differences in profitability or even difference of either. It is first of all only a relative argument, saying nothing about the actions in the grander scale, appliable to all of its kind, but only in relation to one specific action that happened at a past date. Because of that, it is not even a descriptive definition.