I specifically said that "community" which makes "communal decisions" is not anarchy. You've simply claimed it does, then mentioned "governing authority", which is not entirely in line, now is it?
You're right on the strength of my argument, but you're wrong on anarchy not being able to create governments (in the M-W definition above). But I'm not going to argue this any more.
I hope Merriam-Webster clears that up:
"Definition of government
1 : the body of persons that constitutes the governing authority of a political unit or organization"