[sympil]

Anomy is chaos, ruled by the ones with the biggest bats, without any protections against that, for the masses.

Then anarchy as you describe it can not exist. In a power vacuum someone will have the biggest bat and thus be the ruler.

[mr_toad]

Anarchy argues that supreme executive power should not rest in a ceremonially selected individual but instead derive from a mandate from the masses.

Yes that’s paraphrasing Monty Python. But real anarchism isn’t the rejection of all authority, just the rejection of hierarchies of power in favour of ideas of collective responsibility and decision making.

Committees, not Crowns.

[sympil]

…hierarchies of power in favour of ideas of collective responsibility and decision making.

Thus it can’t exist becuase some group will eventually gain more power than others and thus exert control.

[LargoLasskhyfv]

Even if only a purely speculative, theoretical concept, it's still a misnomer to use it as substitue for anomy.