Public key encryption makes possible a world where much of human interaction is unobservable to anyone but the parties involved and those they choose to reveal it to. One consequence could be to put everything online out of the power of government to control — what you cannot see, you cannot tax or regulate. Whether that is a bug or a feature depends on how well non-governmental mechanisms can replace the useful functions of government, in particular law and contract enforcement. Fortunately, the same technologies that make strong privacy possible also enable mechanisms to enforce agreements based on reputation.
Reputational enforcement of a contract depends on interested third parties being able to know, at low cost, who violated the contract, in order that it will then be in their interest not in the future to trust the violator. If the information of which party is guilty is too costly, third parties will instead conclude that one of the two parties cannot be trusted but they do not know which so should avoid both, making it no longer in the interest of the victim of the contractual breach to complain about it.
Digital signatures make it easy to prove to any interested third party that a contract was signed, that it specified an arbitrator, and how the arbitrator ruled. Combine that with a policy of designing contracts to put the opportunity to profit by default on the party with the greatest interest in maintaining his reputation, for instance by terms such as whether payment is made in advance or on performance. If neither party has a reputation to lose, leverage the reputation of someone who does by having each party post a bond in digital cash with a trusted third party.
Such mechanisms should make it possible to maintain a functioning economy under conditions of online anarchy.