The tragedy of the commons is not about how many people abuse the commons, but about the fact that the commons is abusable precisely because there are no property rights in it.
The obvious solution is for fish farms to start raising Omega-3 production, but the fact that the fish in the ocean are unowned means it's still cheaper to overfish, and the only time that won't be true is immediately before the ecological disaster (assuming it is one) of menhaden extinction.
1. the solution to a tragedy of the commons is not always to privatize the common resource. Private firms have historically continued to harvest their privately held resource until gone (e.g., privately held old growth forests in the Pacific Northwest) because they can use the resource (the land the forest once grew on) in some other profitable way.
As long as there continues to be some means of profit from the resource (in forestry, replanted pine tree farms for wood pulp where formerly redwood was harvested; in fisheries, aquaculture or harvest of other species) there is little or no incentive for the private firm to preserve the original resource.
Here, with menhaden, as long as the private firm can continue to harvest something profitable they will have no incentive not to overfish the menhaden till the stock collapses.
The reason is simple; the resource that is publicly beneficial is live menhaden, filtering the water by consuming algae. The resource that is privately beneficial is dead menhaden, pressed for oil and ground for animal feed. This is why public protection is sometimes necessary; because the public good cannot always be made to coincide with private profitability.
2. Fish farming is unlikely to be the answer for the simple reason that farm raised fish are not fed a diet consisting mostly of algae (the primary source of the sought after omega-3 fatty acids). Farm raised fish are, as a result, lower in these beneficial fats than their wild counterparts.
Private firms have historically continued to harvest their privately held resource until gone (e.g., privately held old growth forests in the Pacific Northwest) because they can use the resource (the land the forest once grew on) in some other profitable way.
In such a case, the fact that someone else didn't buy the land with the forests on it suggests that this was the most efficient use of the old-growth forest and the land it was on. That is, just because you or I find the solution unpleasant doesn't mean that it's not the efficient outcome. If it is an inefficient outcome, then there should be a market solution which makes the implementer lots of money.
"The tragedy of the commons is not about how many people abuse the commons, but about the fact that the commons is abusable precisely because there are no property rights in it."
Now this is rather circular reasoning. The tragedy of the commons relies on multiple persons. The whole theory of the tragedy of the commons says, that since you are not sure how much the other person will use the resource, you will use it as much as possible (even if it results in destruction of the resource). The whole reasoning falls apart if there is only one person using it. You must be working from a completely different definition of "tragedy of the commons."
The obvious solution is for fish farms to start raising Omega-3 production, but the fact that the fish in the ocean are unowned means it's still cheaper to overfish, and the only time that won't be true is immediately before the ecological disaster (assuming it is one) of menhaden extinction.