I'm a free-market anarchist* and, not surprisingly, I enjoy writing sci-fi and fantasy stories about societies without governments. However, I do NOT want to write stories that only myself and those who agree with me will enjoy. I'd like to know what would make a government-less society believable for the typical reader of speculative fiction. I've given it a good deal of thought, but I'm sufficiently biased in this regard so it's difficult for me to evaluate what non-anarchists would think of it.
How do I facilitate a reader's suspension of disbelief when the reader likely believes that a world without government would simply be a dystopian hell-on-earth?
Is it simply that I need to include some of the possible negative consequences of anarchy, like perhaps slavery? Or include a protagonist who has been harmed by the system and advocates for the instatement of a just and fair government? I feel that Brandon Sanderson effectively executed the latter strategy in the The Way of Kings: Sanderson is a Mormon, but he wrote an atheist character (Jasnah) that really felt like a true atheist, using many of the arguments that a Dawkins might make.
If you've read and enjoyed Ursula K. Le Guin's The Dispossessed or Robert Heinlein's The Moon Is a Harsh Mistress or Neal Stephenson's Snow Crash or Vernor Vinge's The Ungoverned, feel free to describe what you found believable about those worlds. I enjoyed those books, and I know a lot of people did (the first two won Hugo Awards), so they must have had some success in creating believable worlds, despite describing worlds without governments that aren't purely dystopian.