In this paper, Ostrom summarizes her work on what she calls “polycentric governance.”
As I understand it, the idea is to find alternatives between two models for governing the use of common resources.
No regulation at all, everyone uses as much of the common resource as they see fit.
External coercion, a body with coercive force, such as the state, regulates the use of the common resource.
The tragedy of the commons is supposed to illustrate how the first model will fail, thereby supporting the second model.
Pollution is the example I am most familiar with. If individuals are free to use the air as they see fit, they will pollute. The marginal cost of polluting is lower for each individual than the marginal gain from polluting, so everyone pollutes and the lousy air makes everyone worse off than they would have been if everyone had polluted less. The state solves the problem by regulating the amount of pollution that a car, industrial facility, or household appliance can emit.
It works. Within living memory, you could not see the mountains from Claremont, and not just when there were fires. Now, thanks to some very heavy handed regulation by the South Coast Air Quality Municipal District, you can. Unless there is a fire.
Anyway, Ostrom’s work challenges this by arguing that there are alternative ways of governing common resources. These do not leave individuals free to use whatever they like, but they do not employ state coercion either. Rather, they involve, well, I am honestly not sure how to put it. Government without coercion? Surely there is a price for breaking the rules. Anyway, whatever enforcement there is does not come from a state.
She must surely be right about the basic point. Human societies managed common resources for a long time before there were states.
I am afraid that I am not versed in her account of how it works. However, I can recommend a very elegant theory by David Hume that is in the same neighborhood.
One last point. My guess, and it is only a guess, is that in large societies, most of the non-state means of governing common resources would not work without the protection of states. That is where Hume wound up, at least. As I said, that is absolutely a guess.