Having zero governing bodies is a thought experiment laid out more than a few times in Sci-Fi, so assuming those weren't totally wrong, I don't think the human race can do without. The problem are humans and their motivations. Greed is one problem, laziness another. I don't know how to solve those. How do you make sure people do not exploit their freedom by making others suffer?
Okay, let's say there's no governing body. Now, there's a dispute. How is it resolved? Fight to death? The achievement of modern society is that we do not kill each other, and that requires rule makers, rule enforcers, oversight to keep chaos down to a minimum. If we do, it's a punishable offense. But punishment as implemented right now is totally wrong and doesn't solve anything. Putting people away for years does not make the crime undone and also doesn't turn a killer into a pet store owner. There are experiments with different kinds of containment and reintegration into society but this is also a hard problem that's unsolved.
I honestly don't know how without some sort of management entity a peer to peer society would work without rules of any kind.
Once you enact rules of conduct, you have everyone follow the rules, and something somewhere needs to make sure rules are not broken unjustifiably.
It's like distributed systems or cooperative threading, if you think about it.
Can you tell me how you'd do it?
You've got an excellent question and I've got an excellent answer for you: https://www.youtube.com/watch?v=jTYkdEU_B4o It's a short video, but I highly recommend it to you (skip the first minute or so for a short historical intro). Please come back here and let me know if it answered your question. I also hope it doesn't just answer your question, but sets in your in a different mode for thinking, mode in which problems that seemed unsolvable can now be solved.
So, this all sounds like P2P with an evolutionary system of contracts between all kinds of parties, where there's no universal rule book (aka what we know as a country's laws).
If this really works, good, but how do you solve that humans will see that the contract between two other parties is better and will want the same deal? Will you give it to them?
I'd really like to think this is workable as it would give custom-fit "laws" for everybody. Though, there still needs to be some kind of general laws for heinous crimes, doesn't it?
Not sure I understand the question. Who is giving whom the contract? The idea is, if you don't like the laws your protection agency / law firm provides you with, you switch firms. And that way you have a lot more control under which set of laws you want to live.