Anarcho-capitalistss agree with many things that some utopian anarchists such as William Godwin or left-anarchistss like Michael Bakunin wrote about individualism. However, They don't quite follow Bakunin in his complete acceptance of Karl Marx's Das Kapital. Actually, anarcho-capitalists don't accept the distinction between a "personal" sphere of activity and an "economic" sphere of activity - they only see one sphere, the sphere of Human Action.
Many left-wing anarchists claim their anarchism to be the one, true, oldest and original anarchist tradition, and dispute the right of anarcho-capitalists to call themselves anarchist at all, suggesting instead the terms neo-classical liberal or anti-state capitalist. Most anarcho-capitalists, by contrast, claim that their own anti-statist tradition is at least as old, and much more coherent with their individualist theories than with any of the collectivist anarchist theories.
Anarcho-capitalists consider that libertarian socialist notions about power, hierarchy, authority, etc. are vague and inconsistent. They think it is legitimate for individuals to voluntarily enter a subservient relationship where one submits to authority, presumably in exchange of some other service. What they oppose is the means by which some might compel such obedience, by force or fraud. However, this is like opposing robbery and racketeering in theory, while accepting it in practice.
Anarcho-capitalists consider as ridiculous the want of liberty without ever acknowledging the dual notion of responsibility.
As for property rights and capital rent, anarcho-capitalists agree with Frederic Bastiat (a friend and precursor to Molinari) in the debate he had with the early Pierre-Joseph Proudhon.
Anarcho-capitalists defend the right of individuals to freely organize in cooperatives; but they resent the claim of most libertarian socialists that people should be forced into such cooperatives and that even willing, they should be prevented for their own sake to enter or defend employment contracts. They also think that cooperatives are usually a bad idea, because people are risk-averse, and it is irrational for them to have all one's stock in one company (one's cooperative); they think that workers would rationally seek to spread their risk by diversifying their stock portfolio. See this article about Entreprise in a Free Society.
Like individualist anarchists, anarcho-capitalists think that individuals exist before any collectivity and that no collectivist decision (and they reject a dichotomy between economic and personal matters), may hold without the prior consent of individuals. Anarcho-capitalists thus loathe the 'democratic' kind of collectivist control meant to happen in socialist anarchism, and wonder on which grounds socialist anarchists decide at which scale democracy should be held instead of whichever other scale - and whose opinion is to prevail when there is disagreement.
Anarcho-capitalists think that libertarian socialists either avoid or miss some essential issues concerning justice and protection: judicial prosecution, law-making and law-enforcement - how it is possible to avoid and resolve conflicts in a free society without resorting to any kind of government. They consider that property rights are exactly the conceptual tool required for a justice system to exist without the need for centralized law-making and law-enforcement.
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