Recently my wife and I went on vacation with some friends, and one day a discussion about Libertarianism ensued...as such discussions are wont to do. During this discussion a question was put to me, which was: "If I stand just off your property and yell obscenities day and night, who dispenses justice?"
Now as it happened on this particular day I had decided that I should do my best to consume what alcohol was left in the rental unit, since we only had a day or two before we had to check out. I have no idea how much I had imbibed by the time the discussion began, but it was definitely enough to impair my ability to effectively answer the question as presented...at least to my satisfaction. So, lest my friends think they "got me" on that point, here is the response I would have given, had I had full use of my faculties at the time. ;)
First, the question as worded seems to assume that Libertarianism = Anarchism. Admittedly, this is a comparison which many Libertarians would find agreeable, depending on the individual's view of the legitimate role of the State. Since I happened to be reading Rothbard at the time, I found the question very poignant, as he arguably felt that the State is an entity that can and should be dispensed with whenever possible...which pretty much means "always".
The bottom line, however, is that there must be some system to arbitrate disputes between individuals or groups and in some way punish violations of rights by one against another. This system can take many forms beside the currently accepted form of State-administered justice, with all its waste, corruption, and perverse incentives. In For a New Liberty, for instance, Rothbard outlines a system of private arbitration that is completely separate and independent of the State, and it is indeed compelling.
A more important question, though, is what exactly constitutes "justice" in this case...or rather, what is the injustice that must be put aright? Am I being harmed by the obscenity-yeller, and if so in what way? From a Libertarian standpoint, I am only being harmed if the aggressor is somehow violating one or more of my rights. More specifically, since all individual rights in one way or another are a product of property rights, is the yeller somehow violating my right to private property? I think, yes.
If we go back even further into the origins of property rights, to Locke, all right to property stems from an individual's ability to be productive. This ability grants the individual exclusive rights to dispose of the fruits of his or her productivity in the manner he or she sees fit. Someone standing at the edge of my property yelling obscenities could very well have a negative impact on my ability to be productive. If the yelling is incessant, persisting day and night, I probably won't be able to sleep. This would certainly affect my ability to be effective at my job, possibly causing me to lose some income and resulting in financial harm.
There are other ways I could be harmed as well. I could become ill from lack of sleep, or I could fall asleep at the wheel of my car, thereby harming me physically. In the end, though, both of these impact my ability to produce, and we're back at Locke's viewpoint. By the same token, the yelling would probably affect my ability to use my property as I see fit, as I may not be able to spend time outside my home in my yard without being yelled at.
So, even if we don't consider the possibility of various types of "psychological harm" that might be done to me, there are still several ways that I could be harmed by this aggressor. Any of these would be cause for dispensation of justice by whatever system happens to be in place at the time. Next time, I'll make sure I'm sober before starting an argument.