A common fallacious anarcho-socialist claim is:

“Private property is a State.”

They argue:

A common definition of the state that anarcho-capitalists use is that it is a territorial monopoly on ultimate decision-making power.

A common definition of property that anarcho-capitalists use is that it is ultimate decision-making power.

This makes the ownership of territory, i.e. land, incompatible with anarchy, because it is identical to a state.

There are several easy refutations:

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