Nothing disturbs me as much as the minarchist argument that there is a need for a final arbiter and that this arbiter must be external to the market. Without a final arbiter there will be biases and problems of unjust rulings, and therefore there must be a State, goes the argument.
Ayn Rand utilised this argument, saying a market without a State would degenerate into "civil war." This is the "obvious" result of protection and "violence" services offered freely in the market place — when firms selling coercive services compete, they will use the resources at hand to stifle competition: Violence.
Of course, seen in the light of Randolph Bourne's famously stated truth that "war is the health of the state," Rand's assessment of the market for protection services and the "need" for a State seems ridiculous.
Ridiculous or not, it is still a common argument used by minarchists that the market needs both rules and a ruler. The market sets its own standards and rules, and that is all well, but the enforcement of such rules is the problem. Minarchists cannot see the truth when someone points out that a market might need contract enforcement services and that as a last resort people might need to hire someone to protect their rights to property.
Of course, if people would hire the people known to have guns today (except for State thugs, of course) we would have a problem at our hands. The people with guns today, i.e., the people actually using guns on a daily basis as part of their "job," thrive off other people's misery. They are either State-employed thugs making money forcing people to "obey" in their own "interest." Or they are hired guns working for competing criminal organisations such as the mafia. Both of them are known to kill people as they see fit without remorse and without any responsibility.
But in a free society there would be no State and no other criminal organisations; such organisations couldn't possibly profit off their line of "business" without being able to hide behind the power of central government. So enforcement, protection, and arbitration services would have to be supplied by legit businesses, and as such they would be dependent on providing valuable services to their clients and their reputation.
Some minarchists might accept this as a valid argument, but they would still have a problem with the final arbiter in disputes. There needs to be someone to make a final decision; someone to make sure rules are followed and that property rights are fully protected in accordance to natural or market law. And that someone needs to be completely neutral to supply such services.
This last point, that the final arbiter needs to be completely neutral, seems to be what often confuses many minarchists. To them, for some reason, this implies that the judge or court needs to be external to the market. There is logic in this argument, but it is based on a false understanding or definition of the market.
As is the case today, when business firms cannot agree they turn to a third party to settle the conflict. This third party might be the State, and since the State doesn't have much to do with business firms or other market actors (leaving aside the corporate nature of the state and the fascist regime for a moment) it is supposedly neutral and unbiased.
The problem with this is that it is not the nature of the third party that makes him or her unbiased — it is that party's position with respect to the conflicting parties. Two disagreeing antelopes might ask a baboon to provide a solution to their disagreement, but it is not the fact that the third party is a baboon that makes the baboon unbiased — it is that this particular baboon has no prior relationships, ties or indebtedness to any of the disagreeing antelopes.
Imagine two friends disagreeing to such a degree that they cannot get past this disagreement. Do they need to find a person to solve this conflict who is not anybody's friend? No, they need to find someone who isn't [secretly] a friend of one of them or has any other ties that would make him/her possibly unbiased.
So would two firms disagreeing on how to interpret a contract need to find a non-firm to solve their problem? No, they would probably be able to agree on any firm without ties to either of the parties — and that firm could still be perfectly unbiased and fair. It is not the nature of the arbiter that matters; it is the relations and interests of that specific arbiter that counts.
In the world of States this surely sounds strange. But this is the case simply because States know States — and they would never trust another State. Therefore they make alliances with whatever State is the strongest and establish "international organisations" to solve conflicts between States of equal strength. Even so, States usually don't obey their own rules or rulings of such organisations they have themselves established.
Even ridiculously insignificant States such as Sweden, the State that claims to be my master, is repeatedly condemned by e.g. the European Court of Human Rights for crimes against humanity (torture, for instance — believe it or not). What is the result of such condemnations? Absolutely nothing, except for, maybe, a very short article in one or two newspapers; the people comprising the Swedish government couldn't care less.
But the fact that States behave like villains (excuse me, are villains) should not be an argument against profit-maximising businesses in a free society where there are no States.
The fact is that the final arbiter can be whoever as long as that person or organisation is deemed unbiased and is approved by all disagreeing or conflicting parties. That particular person might even have guns without the situation necessarily degenerating into civil war. The fact is, there are profits to earn in this world, but only for those who serve one's customers and show respect for potential customers. States don't have to bother about such things because they have both guns and popular support to use them — including the support of mini-statists or minarchists.