Anomie versus Anarcho-capitalists

Via Wikipedia

1) Anomie

...in contemporary English means the absence of any kind of rule, law, principle or order. It comes from the Greek an-: against or absence, and nomos: law).

This term was used by the Greeks to define anything or anyone who was against the rules or a condition where the present laws were not applied (illegitimacy, unlawfulness). The contemporary English understanding of the word Anomie differs from how the term was originally defined and used by Greeks and tends to become a synonym of the word Αναρχία (see Anarchy). In Greek there is a difference between the word nomos(νόμος)(law), and the word Arhi(Αρχή)(starting rule, axiom, principle). For example, majority rule is an "arhi" and not a "nomos".

Anomie as social disorder: The word, spelled anomy or also anomie, has also been used to apply to societies or groups of people within a society, who suffer from chaos due to lack of commonly recognized explicit or implicit rules of good conduct, or worse, to the reign of rules promoting isolation or even predation rather than cooperation (consider the Ik tribe). Friedrich Hayek notably uses the word anomy with this meaning.

Anomy as social disorder is not to be confused with anarchy. The word 'anarchy' denotes lack of rulers, hierarchy, command, whereas 'anomy' denotes lack of rules, structure and organization. Many opponents of anarchism claim that anarchy necessarily leads to anomy; however, many anarchists will argue that hierarchical command actually creates chaos, rather than order (e.g., see the Law of Eristic Escalation).

As an older variant, the Webster 1913 reports use of the word anomy as meaning "disregard or violation of the law".

2) Anarcho-capitalists

...promote individual property rights and free markets (in the sense of freedom from government interference) as the most just and effective way to organize all services. They see the definition of property rights through contracts and common law as a universal mechanism to solve conflicts.

They regard capitalist businesses as being the product of voluntary contracts and thus a legitimate and efficient way for people to organize, with freedom to choose a competitor or to enter competition as the universal way to preserve and promote quality in services. This analysis includes all goods and services, including those which the state has traditionally claimed as its natural monopoly — such as police or military forces (though only for defensive purposes) and justice through courts of arbitration.

Thus, anarcho-capitalists hold their position to be a form of anarchism. Anarcho-capitalists repudiate all forms of state control — including taxation, coercive regulation, aggressive war, and coercive monopoly on the use of defensive force — as violations of essential individual rights. They reject these forms of coercive control whether they are exercised by state officials or by private agents; they oppose them on the grounds that they are violations of rights, not necessarily because they are committed by governments.