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Their proposal requires a central bank. They discuss how to do "offline" transactions without contacting this central authority, but double-spending would only

• betterunix 13y ago
  It is worth pointing out that the double spending is not merely detected in these systems; the bank is able to compute a proof, that anyone can verify, of a particular party's guilt. This allows the bank to create a blacklist, or to use a legal system, etc.
• nly 13y ago
  It doesn't necessarily require a central bank, which everyone must be compelled to use, it just requires a banking system. If someone wishes to pay you, and happens to use a different bank to yourself, then your bank (whom you, admittedly, have to trust) can work on your behalf, directly with the sourcing bank, to claim the funds. There's quite good reason to trust in this system because our bank knows that the sourcing bank can identify double-spenders. The plus side of such a system is honest bank customers still get complete anonymity, even if the banks conspire against you. The downside is you can never know if your bank is conspiring against their customers as a whole i.e. by not operating in line with their inflation/reserve policy... which of course is one of Bitcoins best features.