Having spent some time in anarchist communes and so speaking from first hand experience, since there is no above authority to rule conflicts they are solved by having all involved sides talking with each other and finding a common solution. Depending on the cases, it can go to from a "everybody is happy now" resolution to underhanded politics leading one side to be told to shut up and deal with it. But it does work. Limitations being it scales badly with larger group of persons (not sure it can work well above 50 heads) and that some people are broken, can't take decisions by themselves and actually need hierarchy to tell them what to do.It's the same problem you get when you talk to anarchists. Oh great, no government and central authority. So what happens in a conflict? Somehow, all the good anarchists are supposed to gang up on the bad anarchist and make them stop? They'll come up with all these rules, and it's like, oh ok, anarchy only works when there's a central government attached. Makes perfect sense.
In any case it is a very good experience to have that force you to take responsibility for your shit and makes you realize how good life could be.