Free market anarchism has too often been described as "private property anarchism" where supposedly all property is privately owned. In some cases, that description is to imply no property is owned by a state. In this I agree with the implied meaning, but not the term private property anarchism.
Two types of common property could exist in a free market anarchist society. The first is when individuals voluntarily and purposely form some group, party, marriage unit, or company where property is held in common. This is considered acceptable to those who use the term private property anarchism, and it could still be called a type of private property.
The second type is much more complicated. Could it be understood from a private property perspective? Possibly if one is open to the ideas of partial use leading to partial ownership. This is without any prior formal agreements incorporating a potentially imprecise owning group. It is simpler to call it stateless common property.
Attempting to understand this type of common ownership will go great lengths to finding a common ground to open-minded socialist anarchists. Perhaps it is best to begin with an example from Leo Tolstoy's "The Kingdom of God is Within You."
In Russia, at the end of the 19th Century, there was a village that owned a forest communally, and had so for generations. They had used it for hunting and it was a major source of food. The Czar had given this forest to a feudal lord who then outlawed hunting or trespassing on his now private property. When the villagers continued to hunt there as necessary to survive, the Lord had them beaten and flogged in public. At this point any free market anarchist should see the legitimacy of this common ownership over what some socialists would (improperly) call the private property of the Czar. Any form of ownership is illegitimate when created or thus tainted by the state.
An easy way to grasp the formation of legitimate common property is to think of the Crusoe economics of roads. Roads formed long before they could be thought of as owned private property. The fact that early roads needed little to no upkeep was an important factor, and is a common trait to most property that can be said to freely develop from unowned to common property of a group, tribe, village, etc.
An individual did not per se mix his labor with the earth to make many of these primitive roads for private property in the Lockean sense. Individuals qua individuals merely make a road by traveling to some other place. If a person travels once a month from a homestead to a lake twenty miles away on a dirt trail only identifiable as a beaten path, he would have no right to claim the whole path as his excludable private property on which no one may travel or perpendicularly cross.
However, although it would be ridiculous to claim exclusive property in a beaten path, it would be wrong for another person or group to create a homestead completely encircling our first homesteader and claim the first homesteader has no free right to travel as he previously did. Thus, there must exist a natural "right of passage." This could be thought of as partial non-exclusive ownership of land. As others also have a similar partial non-exclusive ownership by use, it is then a common property.
Other cases of non-exclusive ownership share characteristics of common property. Though I may own my homestead, if I have no current or unabandoned prior use of a particular radio frequency (or am actively using their absence), then a radio broadcaster is free to generate them even if they pass through my home without compensating me. I would also have no right over censoring the content of the radio waves that pass through my house except by choosing to not tune into them. On the other hand, as microwaves would actively harm me and my property, there could be no right to pass microwaves through my property as I actively use my property to not be harmed.
It should then be seen that all property is also an ownership through, and limited by, degree of use. Private property is property that entails the right to forbid another's presence. Common property entails the right to not have your presence forbidden for those in the common group. As with radio waves through a homestead, they can exist in the same location in different dimensions, so to speak.
Legitimate common property still has the problem identified by Aristotle as the Tragedy of the Commons. Primitive common property roads may sometimes find benefactors to pay the cost of their upkeep. When so, there is rarely a reason to assume altruistic reasons for this as large businesses may profit more individually from a well kept common road than their cost to maintain it. Nevertheless, it should be expected that private roads would be built where high maintenance costs are required like modern highways, etc. However, these would have no right to be built on top of the common roads and private and common would have to compete. If the demands of roads are expensive enough then the common roads would potentially become abandoned. If so, only then would they cease to be common property and become abandoned homesteadable property and if then made so others could be excluded from use or trespass.
Unanimous support of a community may allow a common property such as a road to be privatized. Yet to do so, it would likely require the private road to guarantee equal passage rights to all to prevent class and privilege rights that would not be a fear with common property roads. Some private roads, in order to compete, may give up the right of exclusion in order to allay fears of discrimination. In which case, a private road could not regain that right without unanimous consent of the community.
Common property can exist in a free market state of nature, ordered anarchy, etc. when: 1. The cost or knowledge for privatized ownership is, at least at the time, too great. 2. When scarcity is not a significant problem. 3. Pollution of the good is not yet a problem. 4. Any other Tragedy of the Common problems are not insurmountable. A watering hole or well used by a primitive village would be another case, as is the air supply before pollution problems.
With a river, the case could be thought of as private property rights in the class of flowing property. If a person is using a clean river area for fishing, others may homestead the river upstream, but they will not have the right to pollute or act as to harm the first user's downstream fishing. But do individuals have identifiable, tradable shares of the air supply? Are they given at birth? So open atmospheric air is (at least in most cases) better thought of as common property. Polluters would be subject to class action torts of the community when harmed without agreed compensation.
So, common property and private property can coexist in the same anarchist society. However, return to Tolstoy's village (A). Assume it had maintained its common ownership of the forest unhindered by any state. A new village B appeared beside it, and B's common use of the forest would make scarcity a serious problem. Then A must prohibit or limit B's use of the forest and the common-ness of the forest would only be for A. It would be both private property and common property in different respects.
There are other potential problems in the nature of non-state common property. Assume villager X decides to kill massive amounts of animals to sell and export food and skins outside the village, making scarcity a problem. In order for a common group to maintain its assets from abuse of its own members, it must have self-enforcing (with respect to the common group) social conventions to prevent abuse. It may make such abuses punishable and not just with ostracism, but with violence if necessary as well.
Villager X is acting to harm the common property of the village, and the rest of the village has the right to stop him. He would be taking more than a "common share." (I recognize the imprecise nature of that term. It is outside the scope of this essay to address it.)
The only insight I have is that, just as in private property, the Principle of Equal Liberty, as described by Herbert Spencer should apply to common property. Perhaps property should be thought not as two categories of owned and unowned, but in three: unowned, non-excludable, and excludable.
Perhaps this essay will engage a more rigorous thinker than myself to complete the all-encompassing systems of Rothbard and Mises regarding this subject. This is one of very few areas to my knowledge of the nature and workings of a free society that our movement has not deconstructed and thoroughly analyzed.
This is not a bibliography, as this essay was thought out before reading the works below. However, in different respects, they grasp and use the idea presented here without fleshing it out. Perhaps it is no coincidence that they both recognize the critical rationalist methodology of Karl Popper in these books.
Anthony de Jasay's Against Politics is addressed to the top academic audience and not directly to the libertarian/anarchist movement. He defends a deontological approach to ethics and politics, rejecting utilitarianism without relying on natural rights. This also addresses social conventions in ordered anarchy.
J.C. Lester's Escape From Leviathan begins with a critical rationalist approach to building anarchism from equal liberty, but concludes that this encompasses more than just private property. This is without the waffling as done by Hayek and Nozick, but with some surprising conclusions.