Kudos to Hal Finney for his descriptions of Stefan Brand's offline cash. As with other offline cash protocols it contains the following assumption:
Let's call the user Irving, and the number which encodes his identity (it might just be his bank account number in this case) we will call I.
What happens when we've caught Irving double spending (or million spending?) Is it guaranteed that Irving will have enough in his bank account to cover the fraud? I don't see any way to guarantee that except for absurdly large security deposits. Also, are bank accounts required to be in True Names so that multi spenders can be caught and punished? If so, how do we prevent the use of numbered accounts, Duncan Frissel's nom de guerre accounts, etc. and do we really want to set up that kind of True Name infrastructure? Also, what about stolen coins? If Irving can succeed in stealing a coin from Jane without her knowledge, Irving can spend it untraceably as many times as he can get away with (perhaps thousands or even millions, depending on what security precautions we layer above the offline cash), and Jane gets fingered. On the other hand, Jane might simply give Irving some coins, plausibly claim they were stolen, and split the proceeds from Irving's spending spree. In general, multi spending might occur because of accident, malice, or a combination of those two factors. How do we distinguish between accident and malice to determine liability, reputation loss and/or punishment?