No. Due to its basis in private property, "anarcho"-capitalism implies a class division of society into bosses and workers. Any such division will require a state to maintain it. However, it need not be the same state as exists now. Regarding this point, "anarcho"-capitalism plainly advocates "defence associations" to protect property. For the "anarcho"-capitalist, however, these private companies are not states. For anarchists, they most definitely are.
According to Murray Rothbard ["Society Without A State", Nomos XIX, Pennock and Chapman (eds.), p. 192], a state must have one or both of the following characteristics:
1) The ability to tax those who live within it. 2) It asserts and usually obtains a coerced monopoly of the provision of defence over a given area.
He makes the same point elsewhere. [The Ethics of Liberty, p. 171]
Instead of this, the "anarcho"-capitalist thinks that people should be able to select their own "defence companies" (which would provide the needed police) and courts from the free market in "defence" which would spring up after the state monopoly has been eliminated. These companies "all . . . would have to abide by the basic law code." ["Society Without A State", Op. Cit., p. 206] Thus a "general libertarian law code" would govern the actions of these companies. This "law code" would prohibit coercive aggression at the very least, although to do so it would have to specify what counted as legitimate property, how said can be owned and what actually constitutes aggression. Thus the law code would be quite extensive.
How is this law code to be actually specified? Would these laws be democratically decided? Would they reflect common usage (i.e. custom)? "supply and demand"? "Natural law"? Given the strong dislike of democracy shown by "anarcho"-capitalists, we think we can safely say that some combination of the last two options would be used. Murray Rothbard, as noted in section F.1.1, opposed the individualist anarchist principle that juries would judge both the facts and the law, suggesting instead that "Libertarian lawyers and jurists" would determine a "rational and objective code of libertarian legal principles and procedures." The judges in his system would "not [be] making the law but finding it on the basis of agreed-upon principles derived either from custom or reason." ["Society without a State", Op. Cit., p. 206] David Friedman, on the other hand, argues that different defence firms would sell their own laws. [The Machinery of Freedom, p. 116] It is sometimes acknowledged that non-libertarian laws may be demanded (and supplied) in such a market.
Around this system of "defence companies" is a free market in "arbitrators" and "appeal judges" to administer justice and the "basic law code." Rothbard believes that such a system would see "arbitrators with the best reputation for efficiency and probity . . . [being] chosen by the various parties in the market . . . [and] will come to be given an increasing amount of business." Judges "will prosper on the market in proportion to their reputation for efficiency and impartiality." [Op. Cit., p. 199 and p. 204] Therefore, like any other company, arbitrators would strive for profits and wealth, with the most successful ones becoming "prosperous." Of course, such wealth would have no impact on the decisions of the judges, and if it did, the population (in theory) are free to select any other judge (although, of course, they would also "strive for profits and wealth" — which means the choice of character may be somewhat limited! — and the laws which they were using to guide their judgements would be enforcing capitalist rights).
Whether or not this system would work as desired is discussed in the following sections. We think that it will not. Moreover, we will argue that "anarcho"-capitalist "defence companies" meet not only the criteria of statehood we outlined in section B.2, but also Rothbard's own criteria for the state.
As regards the anarchist criterion, it is clear that "defence companies" exist to defend private property; that they are hierarchical (in that they are capitalist companies which defend the power of those who employ them); that they are professional coercive bodies; and that they exercise a monopoly of force over a given area (the area, initially, being the property of the person or company who is employing the "association"). Not only that, as we discuss in section F.6.4 these "defence companies" also matches the right-libertarian and "anarcho"-capitalist definition of the state. For this (and other reasons), we should call the "anarcho"-capitalist defence firms "private states" — that is what they are — and "anarcho"-capitalism "private state" capitalism.
Before discussing these points further, it is necessary to point out a relatively common fallacy of "anarcho"-capitalists. This is the idea that "defence" under the system they advocate means defending people, not territorial areas. This, for some, means that defence companies are not "states." However, as people and their property and possessions do not exist merely in thought but on the Earth, it is obvious that these companies will be administering "justice" over a given area of the planet. It is also obvious, therefore, that these "defence associations" will operate over a (property-owner defined) area of land and enforce the property-owner's laws, rules and regulations. The deeply anti-libertarian, indeed fascistic, aspects of this "arrangement" will be examined in the following sections.