Most people are risk-adverse, and conflict inspires the greatest risk of all- to one’s life. Hence why most people are non-confrontational. In most cases the desired outcome of arbitrated compromise is for restitution and/or compensation of the “injured” party, rather than retribution.
In terms of arbitrating disputes, humans have usually found specific methods of fulfilling this need without the requirement of a State body. Typically, it is a cultural or religiously-inspired process. E.G. clan or tribal arbitration in many of the so-called “uncivilized” portions of the world which use external 3rd parties.
An example in the modern world I can think of is that, in the betting industry in England, the bookmakers lay out their terms and conditions to all partaking betters. Among the outlining of the rules and regulations of placing bets, these terms and conditions typically reserve full rights to the bookmakers to void bets and refuse payment whenever they so wish.
Naturally, in the event of a dispute or refusal of payment, the customer would be negatively-impacted by this fact and this, in turn, would inevitably harm the business of bet making in the long.
So all the major bookmaking firms in the UK consensually agree to abide by all rulings made in the event of disputes by IBAS, an independent arbitration service. Some of their rulings go against the bookmakers’ positions and some do not, but by agreeing to always follow IBAS’s conclusions for restitution (and wavering the right to void), bookmakers and customers can resolve issues in a fair and compromising way. This method also helps inspire customer confidence in placing bets and, thus, is mutually beneficial.
Notice that no government agency or government-monopolized legal system is necessary for this process.
To conclude, I will leave you with the words of Mises himself. Simply replace the word “socialism” with “government” and the quote stands well.
“If a man says socialism, or planning, he always has in view his own brand of socialism, his own plan. Thus planning does not in fact mean preparedness to cooperate peacefully. It means conflict.” - Ludwig von Mises, Omnipotent Government