Libertarian Schools of Thought Defined
For such a small school of political theory, libertarianism has a surprising number of subspecies. Sometimes these schools can be poorly defined, and this can lead to some confusion when conversations or discussions about liberty come up. To help with this problem, below there will be a few definitions and distinctions between different sub-schools of libertarian thought.
Minarchy is the school of thought which holds that the state is a legitimate institution, but its only legitimate functions are providing military and judicial protection. Minarchy is the majority position amongst libertarians, and its leading thinkers and politicians in history include F.A. Hayek, Ludwig Von Mises, Ron Paul (although this one is debatable, Paul has alluded to being a voluntarist a number of times), Judge Andrew Napolitano, and Leonard Read.
Voluntarism is a school of thought which holds that all human interactions should occur on a voluntary basis and that no initiation of force is permissible. The logical conclusion of this theory is that the state is an illegitimate institution, and should lead those who hold this position to the stance of anarcho-capitalism. However, due to some inconsistencies in the thought of its leaders, there are also people who hold to this stance who fall under schools such as anarcho-mutualism, anarcho-communism, and anarcho-primitivism. For the sake of keeping this simple, these schools will not be covered here, but links to a basic explanation of each are provided. Great voluntaryist thinkers include Lysander Spooner and Robert Lefevre.
Anarcho-capitalism is the more developed school of thought born out of the theory of voluntarism. Like voluntarists, anarcho-capitalists hold that the initiation of force is never acceptable (holding to the non-aggression principle without exception). Since anarcho-capitalism assumes that all men have a natural right to their life, liberty, and property, capitalism is the necessary economic system to ensure these rights are maintained. Anarcho-capitalists hold that judicial disputes and protection should be handled by private firms, functioning in a similar way as private security and arbitration firms do now, albeit with a complete absence of the state. Anarcho-capitalist thinkers include Murray Rothbard (who coined the term), Hans-Hermann Hoppe, Walter Block, Lew Rockwell, and Robert P. Murphy.
There are some other loosely defined schools of thought (such as conservatarian) within libertarianism, but these are the major groups which libertarianism is/has been divided into.