The self-proclaimed anarchists who proceeded to "direct action at the point of consumption" (translation: smash windows and loot) were left anarchists. They were attacking an abstraction -- the free market - by destroying the specific property of individual shop owners. The owners were guilty of wrongdoing because, well, they were "owners."
This is not American anarchism. Individualist anarchism, the indigenous form of the political philosophy, stands in rigorous opposition to attacking the person or property of individuals. The philosophy revolves around the "Sovereignty of the Individual"--as an early champion, Josiah Warren, phrased it. Whether you prefer the term 'self-ownership' or 'the non-invasion principle,' the core of the philosophy remains the same.
The idea is that every peaceful individual must be at liberty to dispose of his person, time, and property as he sees fit. Force is permissible only in self-defense and only when directed at the offending individual(s), not at the representatives of a class. Individualist anarchism rejects the State because it is the institutionalization of force against peaceful individuals.
-Wendy McElroy, "Anarchism: Two Kinds"
The libertarian creed rests upon one central axiom: that no man or group of men may aggress against the person or property of anyone else. This may be called the "nonaggression axiom." "Aggression" is defined as the initiation of the use or threat of physical violence against the person or property of anyone else. Aggression is therefore synonymous with invasion.
-Murray N. Rothbard, For a New Liberty: The Libertarian Manifesto
Market anarchism is a continuation of the natural law ideal, taking it to its logical extreme. Under the classical republican ideal, the state is the protector of the rights of men. The state provides those services needed to secure rights - police, courts, defense - and the people in exchange pay taxes for those services. Where market anarchists dissent is that the state shuts down the market for competition in those services (violating the right to liberty) and extracts payment for the services it does provide under threat of violence (violating the right to property). Instead we argue that even the services of police, courts, and defense, even the provision of the law itself, should be voluntary, no different from choosing a phone company.
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The other set of market anarchists, those who do not come from the natural law tradition, comes from the utilitarian perspective of men like John Stuart Mill and Jeremy Bentham. They argue that the just society is one that maximizes the happiness of its people, similar to Aristotle's arguments in Ethics and Politics. These anarchists point out that the state necessarily shuts down competition in the provision of services, no matter how small the state is. When the state shuts down competition (or to put it another way, creates a monopoly) in the provision of a good or service, the customers are denied the ability to seek those services elsewhere. Since the foundation of improvement in services is competition among providers, shutting down the market for the provision of services in such things like courts and police denies improvement in those services.
- Joshua Holmes, " What is Market Anarchism? - an introduction"
We cannot deny reality. We cannot pretend that slavery is freedom, that war is peace, that the State is our servant, rather than our master. We must choose between freedom and slavery. That is The Choice: liberty, or The State. The Choice: life, or death. The Choice: Our lives, to be lived as we wish; or Orwell's famous jackboot, crushing our faces forever.
-John Lopez, "The Choice"