You would want to use modern technology to record the shit out of everything around you at all times

You would generally want to stay in spaces nobody can access without being identifiable

If you leave these spaces, you'd want to be heavily armed, or at least avoid being a target

If anyone kills a loved one of yours, you'd kill them yourself without relying on a court

If you kill anyone without video proof of them killing one of your loved ones, you could expect to be ostracized or killed yourself in revenge

If you get the wrong person, you might get killed in revenge yourself

If you get the right person, you still might get killed in revenge yourself, just like you might get wrongly killed in a world with cops

This system could be better than having cops, if enough dumb people died and survivors were smart enough to make reasonable decisions when analyzing each other's actions with the info available