As someone who is personally a minarchist, I'm wondering how the Non-Aggression Principle would be enforced in the AnCap model.
Given that there definitely is definitely no executive branch, people would obviously have to take personal defence into their own hands. But would there be trials for people who pollute your land? Surely not all 'aggression' is the type that would give you the right to shoot someone on the spot?
On another note, what about defense from external forces? You would need an organised and unified military. While I hate the government, I cannot understand the AnCap solution to an armed conflict with another country .
Ostracism Many things are under a contract basis. There will be some common things throughout the society such as don't rape or kill. If those are done a person may lose their homes.
Ostracised where to? You would be violating the NAP if you sent them into another's land.
Where they go is up to them but if they violated their current contract(s) then they're out.
By ostracising you are making someone have to enter the land of a another country and the other country will hold you accountable. This does not seem like it would hold up well in the long term.
It Doesn't need to be another "land." In a society where everything is privately owned it could be somewhere down the street. You don't make them did anything. Somewhere is willing to accept him. Somewhere will be ready for this type of person who committed crimes. It's not aggression.