Despite some really big exceptions, like taxation and conscription, our current system of democratic government, at least originally, had the same basic idea as its goal as is behind the ZAP.
Quite true. The seed of destruction was the faulty idea that an agency of coercion (i.e., government) could safeguard those ZAP ideals. Thus the US democratic government was doomed ab initio, by its internal contradiction.
What defines our current system as distinct from the AnCap ideal, therefore, is not their shared idea that individuals have rights and are not creatures of the state - but rather, the exceptions to the ZAP that our system allows.
Bingo.
Thus, the point is that an AnCap system, in practice, is going to be defined, not by the ZAP, but by how arbitration works within it, since that's where the "exceptions" - that may not be the right word - to the ZAP are going to come from.
This does not follow. Assuming
arguendo, that Belters mostly adhere to the ZAP as a first principle, then arbiters will do so as well. Why? Because they will not be hired by litigants if they do not.
Also, everyone keeps assuming that "arbiter" is some sort of professional caste. It is not.
Anyone can sit it arbitration. ANYONE. In EFT, Pablo Rosenberg is probably the closest thing to a professional arbiter. With Reggie, on the other hand, arbitration is a sideline to his church activities--much as rabbis play the role of arbiter in the resolution of disputes between Jews.
Let's create a simple example. Robyn borrows a blouse from Libby to wear to a party. A clumsy boy spills wine on the blouse, creating a permanent stain. Libby wants Robyn to buy her a new blouse (the "you break it, you buy it" theory); Robyn thinks that Libby assumed the risk by lending it to go to a party. (Also she advances the theory that she is not responsible for the stain (the "I didn't stain the blouse, the oaf did" theory).
Rather than fight about it, they decide to ask Emily to resolve the issue and agree to abide by her decision. Emily agrees to act as arbiter (for free or for .2 grams of gold). She decides that Robyn should pay half the cost of replacing the blouse. Neither Robyn nor Libby are crazy about the solution, but a deal is a deal. Problem solved. Now is Emily secretly aspiring to be a member of the putative oligarchy that does/will rule Ceres? Probably not.
Under AnCap, you can't just ignore the existence of other people either, and so the form that arbitration will take will make a very big difference to the kind of society you will be living in - so if arbitration is handwaved away as "something we'll figure out later", the objection that AnCap is a pig in a poke is a legitimate one.
If the ZAP is the Belters' First Principle, then mutually agreed upon arbitration to resolve disputes, is the Second Principle. Why? Because it is pretty much the only form of dispute resolution that does not, explicitly or implicitly, involve the initiation of force. (I say "pretty much the only form" because, there are even more primitive alternatives, such as paper-scissors-stone or running a foot race.)
BTW, trial by combat, trial by ordeal or throwing the I Ching are all permitted by the ZAP. For a resolution based on the merits, though, some sort of voluntary third-party resolution is the only ZAP-compliant option.
And just to tie this up, voluntary means voluntary. If someone does not agree to arbitration, his life will suddenly become a lot more complicated.