Yes, but the differences are sometimes rather academic. One division concerns the justification of libertarianism. There is an ongoing discussion between natural rights theorists like Rothbard, and utilitarians like David Friedman. A parallel discussion pits natural righters against contractarians like Jan Narveson.
Other divisions concern strategy in bringing about a libertarian society. There are a few parliamentarians among anarchists, but most take the Voluntaryist position and refuse to vote or participate in electoral politics. Lysander Spooner argued that voting could be a valid form of self-defence against the predations of the State. Rothbard was a parliamentarian, always involved in political coalitions and electoral politics; George H. Smith and Wendy McElroy are strongly opposed to feeding the beast.
Agorists believe that counter-economics (using black and grey markets, that is, the underground untaxed economy) is the path to a free society. Samual E. Konkin III founded this “libertarian left” philosophy. His pamphlet The New Libertarian Manifesto is the classic presentation of this anti-establishment framing of anarcho-capitalism.
Some anarcho-capitalists have actually shunned the term “capitalism” and describe themselves as “left libertarian” free market anti-capitalists! Why? They choose to use the nineteenth century Marxian definition of capitalism — the exploitative collusion of (certain established) capitalists and State. (Most anarcho-capitalists would call this “economic fascism” or “statist capitalism.”) This approach is basically a marketing ploy; branding anarcho-capitalism in a way that may attract anti-privilege lefties who use such jargon. These “left libertarians” tend to stress anti-corporation and equality issues, as their lefty jargon would imply. Some may even call themselves “socialist,” again appealing to nineteenth century terminology. Brad Spangler suggests, perhaps tongue in cheek, using the term “stigmergic socialism.”
A high-profile division among anarcho-capitalists concerns ”what things can be valid property”. In particular, the validity of intellectual property (IP) is hotly contested, with one camp per Benjamin Tucker denying that non-scarce goods qualify as property, and the other per Lysander Spooner strongly supporting copyrights and patents. Agorism, mentioned above, is anti-IP. Another property question is whether land and natural resources are valid private property. While most anarcho-capitalists consider land to be valid property, geoanarchists disagree. Geoanarchism is the radical branch of geoism (or Georgism), which interprets the Georgist “single tax” ground rent as either a “citizen’s dividend” to be disbursed to everyone in the community, or as the income to a community-owned firm providing municipal services.
Finally, there are esoteric arguments about speculations on ”what a stateless society would look like.” Will PDAs (Private Defence Agencies) be vertically integrated, or would there be separate police, court, and penal firms? Will there be non-territorial provision of defence, or will it be provided in territorial enclaves, such as neighbourhoods, wards, and quasi-city-States? The latter is called Heathian anarchism, after Georgist dissenter Spencer Heath.
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