It should first be noted that the paradox of the "Tragedy of the Commons" is actually an application of the "tragedy of the free-for-all" to the issue of the "commons" (communally owned land). Resources that are "free for all" have all the problems associated with what is called the "Tragedy of the Commons," namely the overuse and destruction of such resources; but unfortunately for the capitalists who refer to such examples, they do not involve true "commons."
The "free-for-all" land in such examples becomes depleted (the "tragedy") because hypothetical shepherds each pursue their maximum individual gain without regard for their peers or the land. What is individually rational (e.g., grazing the most sheep for profit), when multiplied by each shepherd acting in isolation, ends up grossly irrational (e.g., ending the livelihood of every shepherd). What works for one cannot work as well for everyone in a given area. But, as discussed below, because such land is not communally managed (as true commons are), the so-called Tragedy of the Commons is actually an indictment of what is, essentially, laissez-faire capitalist economic practices!
As Allan Engler points out, "[s]upporters of capitalism cite what they call the tragedy of the commons to explain the wanton plundering of forests, fish and waterways, but common property is not the problem. When property was held in common by tribes, clans and villages, people took no more than their share and respected the rights of others. They cared for common property and when necessary acted together to protect it against those who would damage it. Under capitalism, there is no common property. (Public property is a form of private property, property owned by the government as a corporate person.) Capitalism recognises only private property and free-for-all property. Nobody is responsible for free-for-all property until someone claims it as his own. He then has a right to do as he pleases with it, a right that is uniquely capitalist. Unlike common or personal property, capitalist property is not valued for itself or for its utility. It is valued for the revenue it produces for its owner. If the capitalist owner can maximise his revenue by liquidating it, he has the right to do that." [Apostles of Greed, pp. 58-59]
Therefore, as Colin Ward argues, "[l]ocal, popular, control is the surest way of avoiding the tragedy of the commons." [Reflected in Water, p. 20] Given that a social anarchist society is a communal, decentralised one, it will have little to fear from irrational overuse or abuse of communally owned and used resources.
So, the real problem is that a lot of economists and sociologists conflate this scenario, in which unmanaged resources are free for all, with the situation that prevailed in the use of "commons," which were communally managed resources in village and tribal communities. E.P. Thompson, for example, notes that Garret Hardin (who coined the phrase "Tragedy of the Commons") was "historically uninformed" when he assumed that commons were "pastures open to all. It is expected that each herdsman will try to keep as many cattle as possible on the commons." ["Custom, Law and Common Right", Customs in Common, p. 108f] The commons, in fact, were managed by common agreements between those who used them. Similarly, those who argue that the experience of the Soviet Union and Eastern Block shows that "common" property leads to pollution and destruction of the resources also show a lack of awareness of what common property actually is (it is no co-incidence that libertarian capitalists use such an argument). This is because the resources in question were not owned or managed in common — the fact that these countries were dictatorships excludes popular control of resources. Thus the Soviet Union does not, in fact, show the dangers of having "commons." Rather it shows the danger of not subjecting those who control a resource to public control (and it is no co-incidence that the USA is far more polluted than Western Europe — in the USA, like in the USSR, the controllers of resources are not subject to popular control and so pass pollution on to the public). The Eastern block shows the danger of state owned resource use rather than commonly owned resource use, particularly when the state in question is not under even the limited control of its subjects implied in representative democracy.
This confusion has, of course, been used to justify the stealing of communal property by the rich and the state. The continued acceptance of this "confusion" in political debate is due to the utility of the theory for the rich and powerful, who have a vested interest in undermining pre-capitalist social forms and stealing communal resources. Therefore, most examples used to justify the "tragedy of the commons" are false examples, based on situations in which the underlying social context is radically different from that involved in using true commons.
In reality, the "tragedy of the commons" comes about only after wealth and private property, backed by the state, starts to eat into and destroy communal life. This is well indicated by the fact that commons existed for thousands of years and only disappeared after the rise of capitalism — and the powerful central state it requires — had eroded communal values and traditions. Without the influence of wealth concentrations and the state, people get together and come to agreements over how to use communal resources, and have been doing so for millennia. That was how the commons were managed, so "the tragedy of the commons" would be better called the "tragedy of private property." Gerrard Winstanley, the Digger (and proto-anarchist), was only expressing a widespread popular sentiment when he complained that "in Parishes where Commons lie the rich Norman Freeholders, or the new (more covetous) Gentry overstock the Commons with sheep and cattle, so that the inferior Tenants and poor labourers can hardly keep a cow but half starve her." [quoted by Maurice Dobb, Studies in the Development of Capitalism, p. 173] Colin Ward points to a more recent example, that of Spain after the victory of Franco:
"The water history of Spain demonstrates that the tragedy of the commons is not the one identified by Garrett Hardin. Communal control developed an elaborate and sophisticated system of fair shares for all. The private property recommended by Hardin resulted in the selfish individualism that he thought was inevitable with common access, or in the lofty indifference of the big landowners." [Colin Ward, Op. Cit., p. 27]
As E.P. Thompson notes in an extensive investigation on this subject, the tragedy "argument [is] that since resources held in common are not owned and protected by anyone, there is an inexorable economic logic that dooms them to over-exploitation. . . . Despite its common sense air, what it overlooks is that commoners themselves were not without common sense. Over time and over space the users of commons have developed a rich variety of institutions and community sanctions which have effected restraints and stints upon use. . . . As the old . . . institutions lapsed, so they fed into a vacuum in which political influence, market forces, and popular assertion contested with each other without common rules." [Op. Cit., p. 107]
In practice, of course, both political influence and market forces are dominated by wealth — "There were two occasions that dictated absolute precision: a trial at law and a process of enclosure. And both occasions favoured those with power and purses against the little users." Popular assertion means little when the state enforces property rights in the interests of the wealthy. Ultimately, "Parliament and law imposed capitalist definitions to exclusive property in land." [E.P. Thompson, Op. Cit., p. 134 and p. 163]
The working class is only "left alone" to starve. In practice, the privatisation of communal land has led to massive ecological destruction, while the possibilities of free discussion and agreement are destroyed in the name of "absolute" property rights and the power and authority which goes with them.
For more on this subject, try The Question of the Commons, Bonnie M. McCoy and James M. Acheson (ed.), Tucson, 1987 and The Evolution of Co-operation by Robert Axelrod, Basic Books, 1984.