You made a promise. I claim you have broken it. You deny. Who is right?
The standard way to solve such a problem is arbitrage. We have to find a neutral arbiter, who can decides about this.
But it is better to find such an arbiter before the conflict arises. Simply, in this case there will be no argument about the choice of the arbiter.
The way it is done in the network is simple: Once you make a promise, you also have to define some other people you trust, who, in case of conflict, can be used as arbiters.
At a first look, this seems one-sided. You can name your best friends as arbiters. Why should you name some neutral arbiter? Let's see what happens.
I think you have named your best friends as arbiters, and I don't trust them. In this case, I should not rely on your promise. That's all. No conflict.
The point is that you have made your promise for a good reason: You want other people to believe that you will hold the promise. If I don't trust your judges, you have not reached this aim, at least for me.
Maybe I'm prejudices without good reason. Then other people will trust your arbiters, and this is sufficient for you. In this case, you have reached your aim: They believe your promise, and cooperate with you.
But if your arbiters are really unreliable, nobody will trust them, and you find nobody to cooperate, because nobody believes your promise. In this case, you have failed to reach your aim. The solution is obvious: You have to accept some more neutral arbiter, not one of your best friends, but somebody trusted by other people like me to be neutral.
But, of course, you will not accept arbiters who are prejudices against you. This would be too dangerous: Better no cooperation than a cooperation where you may be unjustly penalized for breaking it.
That's why the arbiters who will be accepted will be, at least in part, neutral arbiters.
Everybody can be an arbiter. All what is necessary is that somebody else names you as an arbiter to decide about his promise, and you are arbiter. And all what is necessary for you to make an actual arbitrage is that somebody else asks you to decide about his claim that that promise has been broken.
Of course, make such a decision takes some time and work. You will not do it for free, at least not in the long run. So you will establish some rules: Who has to pay you, and how much, and all the other conditions of your arbitrage. These are your rules, your own promises.
What if you violate your own rules? Of course, nobody will believe you before you accept some neutral arbiter. Thus, if somebody thinks you have broken your rules, he can file a complaint to the arbiter you have accepted.
And so on. Everybody has his own rules, and everybody accepts some arbiters. Yes, arbiters, because there may be many of them. This increases the probability that somebody else will cooperate with you based on your promises: For this, it is sufficient that he trusts at least one of the arbiters.
In the network, there will be nobody left without an arbiter. So there is no "highest court" which is infallible by definition. There is no necessity for such a highest court.
That means there have to be circles: We write a list, beginning with you, then we put your arbiter on it, then his arbiter, and so on. The number of different names is finite, thus, after some time we find somebody who is already on our list. This repetition means we have found a circle. Is this problematic? Not at all. At worst, they all may be close friends, but this is in no way different from the general problem of naming close friends as arbiters.
May be this is a problem: I don't like your decision as an arbiter, go to your arbiter. I don't like his decision to, and go to the next item in the list. Once we have a circle, this never finishes. So what about the initial decision?
This depends on the rules. Maybe, it becomes final immediately. Maybe it becomes final after the first revision. If the third instance finds it wrong, it may require the arbiter who has made the wrong decision to pay a compensation to the unjust victim of his arbitrage. It would be stupid to use rules where the decision never becomes final, and there is no reason to do this.
That there is no "highest court", but only lot's of different arbiters, nobody having any privileges in comparison with the others, does not mean that there will be no structure. Instead, it is quite likely that some quasi-hierarchical structure appears, with arbiters specialized for the consideration of first order appeals or second order appeals. But this is not a formal hierarchy, because there will be no central instance which defines the status of some arbiter in this pseudo-hierarchy. It is simply the natural hierarchy of authority based on competence.