|OK, John, I've mulled it over, and read the other comments here, and so here goes with a clarifying example:|
Would something like this be a satisfactory example of what you consider an extremely minarchist "monopoly of law"?
We, the newly reformed United Free States of America, declare a "monopoly of law" under the following defined geographic jurisdiction [boilerplate description of territorial boundaries].
We have essentially only one law, but it is a big one: "Every individual, while within our defined geographic borders, who is a "citizen" (i.e. is an accepted subscriber to our code of law) agrees to not initiate force against any other human being, but shall be entitled to engage in such retaliatory force against an initiation of force as is necessary to defend their absolute right to not be subjected to an initiation of force."
[Long detailed boilerplate defining all the terms above, and giving a rather exhaustive list of clarifying examples of what is or is not an initiation of force and what is or is not a permissible defensive retaliation against such an initiation of force.]
Enrollment as a citizen in this code of law is entirely voluntary, as compulsory enrollment would be an initiation of force. Citizens will be charged a fee every X number of months in the amount of X standard gold units for enrollment, to pay the costs of administering this code of law. Payment is voluntary -- but non-payment will mean disenrollment from this compact, resulting in non-payors being non-citizens not protected by this code of law.
The administrators of this compact may decline to enroll people who apply for citizenship, or disenroll them from coverage, for noncompliance with the terms of this agreement.
For your convenience, every citizen may, but is not compelled to, enroll in our standard code of law enforcement service. Citizens may decline this enforcement service (since compulsory enrollment would be an initiation of force on our part) and may use some other provider service that fully complies with this code of law, or may arm themselves and self-provide this enforcement service.
Similarly, every citizen may, but is not compelled to, enroll in our standard code of law dispute arbitration service to resolve differences of opinion about how this code of law is to be applied. Citizens may decline this code of law dispute arbitration service (since compulsory enrollment would be an initiation of force on our part) and may use some other provider service that agrees to fully comply with this code of law.
Non-citizens are free to live in these geographic borders, so long as they continue to comply with our code of laws. These non-citizens may do whether the heck they want to, to other non-citizens -- but rest assured they better comply with our code of law for our citizens -- or else.
Competing law enforcement or dispute resolution agencies are free to ply their trade within our borders, and offer to enforce or interpret codes of law that differ from ours, and apply those to non-citizens, but they better comply with our code of law for our citizens -- or else.
In short -- our citizens, so long as they comply with our code of law about non-initiation of force, are free to live their lives within our geographic borders anyway that they please so long as that conduct is consistent with our code of laws, and anyone or any organization whatsoever that violates their absolute right to live that way can expect consequences that will ensure their chastened future non-molestation of citizens, assuming their existence has not been terminated. Your behavior toward non-citizens is up to you -- we don't care what happens to them, because to intervene would be an initiation of force on our part.