Thanks for asking the question. You made me think and learn about something I was not aware I did not know.
Wikipedia defined anarchy as much more than just the social disorder I thought it was:
Anarchy (from Greek: ??????? anarchí?, "without ruler") may refer to any of several political states, and has been variously defined by sources. Most often, the term "anarchy" describes the simple absence of publicly recognized government or enforced political authority. When used in this sense, anarchy may or may not imply political disorder or lawlessness within a society. In another sense, anarchy may not refer to a complete lack of authority or political organization, but instead refer to a social state characterized by absolute direct democracy or libertarianism.
Absolute direct democracy sounds like quite a concept. I cannot imagine it actually working beyond a small group.
To answer the question-- I do not want to say anarchy but that is my answer. No matter who the dictator is I'm deciding, having someone else have control over my life in that fashion would never make me happy even if well-meaning.