Once one gets past Miss Rand's typically vitriolic rhetoric (which only indicates that Miss Rand is quite hostile to what she mislabels as "competing governments") one finds that she has essentially one argument. Miss Rand asserts that what is properly designated as "competing agencies of retaliatory force" or a free market of justice would not work, because the competing agencies would end up protecting criminals and shooting it out with each other. One can only term this a straw man argument.
The situation which Miss Rand "describes" is patently absurd. If competing agencies of retaliatory force protected criminals, they would not be competing agencies of retaliatory force at all. Rather, they would be criminal gangs, plain and simple.
Further, it would be sheer insanity for individuals "subscribing" to competing criminal gangs to live on the same "turf." In this respect, Miss Rand is correct. However, what I and every other advocate of a society without coercion are advocating are not "competing governments" (a misnomer) or "competing criminal gangs" (an ethical monstrosity), but "competing agencies of retaliatory force," which Miss Rand has in fact not dealt with at all.
In the situation described above, in which neighbors subscribed to competing police departments, what is certain (if they were in fact police departments operating on the basis of objective law, rather than criminal gangs operating on the basis of mob rule — which is what Miss Rand described) is that Police B would accept the validity of Police A, or in fact the validity of any reputable police department, and cooperate with them in the arrest of Mr. Jones. Police B certainly would not protect Mr. Jones from justice if there was objective evidence that Mr. Jones had committed a crime, nor would Police A proceed to attempt to arrest Mr. Jones unless there were such evidence. In this manner, objective law would eliminate coercive "shootouts."
Once competing police departments begin to function, standard operating procedures would be created to deal with such cases. At least two possible procedures come to mind: either by stipulation, the police department to which a man subscribed would be the only one which could incarcerate him; or, by stipulation, the police department where the complaint was filed would incarcerate him.
In the extreme, there would be little motivation for policemen to put their lives on the line for a suspected thief, and if competing police departments operated as Miss Rand falsely pictures, then they would quickly go out of business due to the attrition rate of policemen killed in the "line of duty."
This is only one of the flaws of Miss Rand's argument. Other problems include her failure to explain exactly how government can morally outlaw competing agencies of retaliatory force, or what it is that prevents the state police from shooting it out with the county police in similar situations. Clearly, both Miss Rand's premises and logic are in error in this case.
When you get to 35+ you officially get to start calling people youngster. At least, I've declared it so. 
