Government is Irrational.

[Koolay]

I think the first thing that would need to be established is whether or not X recognizes the authority of the court. Or maybe whether or not Y can compel X to show up and face his accusers.

And if the court does have authority to compel people to show up, authority to render verdicts, and authority to see that these verdicts are adhered to.... guess what?
You've just started a government!

No, the 'government' is a violent monopoly that initiates force against people to acquire resources. Justice arbitration is just one product they offer (and badly at that) to distract us from them cutting our wallet in half.

Arbitration will be decided upon by the free market, people are bound to their insurance companies and the DRO court.

You are against taxation? So, who will pay for the roads, hospitals, infrastructure, etc? Who writes the rules without government? Who will enforce it? Better yet, who will enforce without any kind of revenue? Are you certain that every human will cooperate in a positive manner?

Who communicates with foreign countries? Who establishes trade and supply and demand? How will your lack of government determine goods and services needed for society? How will lack of government establish national defense, should other countries want to attack? Just because you think your society can coexist, does not mean other societies will embrace your philosophy.

Your statements, although highly idealistic in nature, omit one important aspect visible in our society. How will you motivate people to work or coexist? Furthermore, without any infrastructure, you doom your society to failure. Unless bridges get built by divine influence.

You curse individuals as slaves for wanting to coexist in society, yet you fail to provide a viable alternative.

If I answered all of this, I would be completely arrogant and way over my head (the government).

The point is, in free market anarchy, is that none of us claim to know what the people want, the people will decide what the people want through voluntarily supporting goods and services. If you think of any function the state provides, there will be millions that will do that for a buck. The free market is the collective genius of 7 billion people, it's power is held back by violent people throughout history, and today most prominently those under the banner of statism. For every question you ask, there would be an expert in that field trying to please those demands because his livelihood depends on it- Rather than a bunch of out of touch old men playing god- THAT is the power of the free market. The people know best.