This is a major flaw of AnCap & NAP as a potential system. Until the human nature of people trying to dodge the rules at others expense is dealt with, a voluntary society will just fall apart into chaos...
http://yourlogicalfallacyis.com/appeal-to-nature...and guess what shows up in the wake....... The State. Where you don't get to choice what is your responsibility or not.
http://yourlogicalfallacyis.com/slippery-slope...and the funny part that you want a State in order to solve the possible eventual problem of getting a State
I personally think we can easier determine between reasonable people what these basic responsibilities are, and come up with rules/laws to enforce them. AnCap thinks these are a choice, but in fact they are not if you want a functioning and thriving society. You need a basic environment/foundation for people to build and evolve on.
http://yourlogicalfallacyis.com/strawmanAt least most AnCaps agree there are rules, they are just determined by an infinite set of voluntary market transactions and the social ostracism of "bad actors" (or people who choose systems opposing to yours), rather than the arbitrary decrees of a handful of politicians of whom were never agreed upon by everyone affected. (Obama was elected by about 1/6th of the USA, as only 1/3rd of Americans even voted. Congressional and local elections have even lower turnouts on average).