There really is not one. Even things like unions, water, fire or homeowners' associations are really special purpose governments. They derive their powers from the governmental body that delegates police power to them.
Even "voluntary" associations that can enforce welfare optimality derive their authority from the government and can only enforce through the courts. The only real exception would be where the Coase theorem would apply and that isn't a free market defense. Rather, it says that rational people will accept transferrable utility, side payments or bribes in such a way that optimal output will not be impacted.
The problem is that "good" solutions do not generally exist to these type of problems. Instead, there are a set of less inefficient solutions. All of the possible less inefficient solutions involve police power. How much police power is useful is an important question, but police power underlies all free markets. Free markets do not exist in the absence of police power.
Still, the use of police power is a costly use of resources and so there are two desired elements of police power. The first is that no more power is in use than is needed at the moment. The second is that a large level of reserve power exists to meet emergencies. This is a difficult problem to balance.
In its simplest form, you want to send the appropriate size response for a home on fire and no more. You don't want sixteen fire engines for a two bedroom home. On the other hand, if you have a large chemical plant in the city, you want to be capable on short notice to respond to a catastrophic accident with the release of hazardous materials and explosion risk and the presence of fire. For a smaller sized town this is almost a contradiction.
The size of governmental response to a catastrophe would require maintaining substantial immediate reserves, well in excess of actual need. Nonetheless, if the failure to respond adequately would be the loss of hundreds of homes and lives then not carrying that capacity is irresponsible.
Generally free-market people have a bias downward, which makes emergency responses difficult, due to the fear of overreach. Over the years, since I know many free market people, I have come to conclude that most of them have a strong emotional reaction to government and they wrap their thinking in a logical manner around this emotion. I think a few of them recognize this is nothing more than preferences in action, but I think most don't realize how much their emotions govern their rationality.
I am biased toward the libertarian view, in the sense that I believe the hand of government should be designed and biased to be the softest possible response that is effective, but I don't have a problem or struggle with solving the public goods problem with government. I do believe that rational oversight by voters is the only solution because the system will reshape itself to accommodate the government with the intent of defeating social efficiency. I also don't believe rational oversight by voters is a good solution, just better than a system on autopilot.
I don't think that questions on the free-market/libertarian/objectivist movement are intellectual in nature and not really a serious question in economics. They are political and emotional. The problem of external costs and inefficiencies isn't a controversy in economics. Now, mechanism design is a serious issue in economics. How to minimize things like regulatory capture and voting inefficiency are serious issues, but the use of government or government authorized bodies is not.