Can you have an Anarchist Government in your story world?

Technically, an anarchist government is an oxymoron.

In order for there to be any sort of government, someone has to be in charge, or be appointed to authority, or nominate themselves to authority. As soon as this happens anarchists would have another authority figure to fight against. Therefore, any society that appeared totally without any authority figures, would, in reality, be run by secret authority figures in the background, whether appointed or self appointed. Therefore, any government that called itself ‘anarchist’ would in effect be dystopian.

It’s an interesting idea, but to make it work I guess you would have to impose other rules or criteria.  The film, The Purge, is a great example of how a dystopian government could use anarchy to control the masses.

Having said that, I like the ancient Greek idea of democracy: every year or so, the voting population could elect one of their leaders to be banished. Maybe not an anarchist government, but certainly a government shaped by organised anarchy – similar to the effect the Brexit vote has had on UK politics.