That’s probably the natural conclusion of anarchy so yes, in most cases that is what would happen.

The word “minarchy” applies well, and I think it’s much more approachable than anarchy. 

The one distinction I’d make is that an anarchist probably wouldn’t support voting, since it wouldn’t be useful to society. Economic and legal interactions would be on a voluntary basis. 

For instance, if my neighbor doesn’t want to pay for the private police to protect his house, that’s his right. But then the police won’t come and he’ll have to protect himself. There would be tons of different, competing models for how to structure this type of a system, and it would never end in a uniform, “one size fits all” outcome.

This is a bit strange to say - but I think anarchy is a better reflection of reality. Extremely strong and tyrannical governments overshadow this reality, but we’ve always been free to interact with others in whatever way we wish. 

Even today, I could choose to not pay taxes, not vote, protect myself, and reject laws I find unlawful. The reason why I don’t is because there is a giant state apparatus which would likely crush me. 

A real anarchist just wants to live in a world where trade and ideas are the standards of living, not theft and violence. And they are usually willing to take risks and push boundaries to create that world.