Good catch on Cox's theorem; that is now fixed. Do you know if the dutch book argument corresponds to a named theorem?

I'm not sure exactly how your comment about deterministic vs. non-deterministic agents is meant to apply to the arguments I've advanced here (although I suppose you will clarify after you're done reading).

Separately, I disagree that the assumptions are unfair; I think of it as a particularly crisp abstraction of the actual situation you care about. As long as pseudo-random generators exist and you can hide your source of randomness, you can guarantee that no adversary can predict your random bits; if you could usefully make the same guarantee about other aspects of your actions without recourse to a PRG then I would happily incorporate that into the set of assumptions, but in practice it is easiest to just work in terms of a private source of randomness. Besides, I think that the use of this formalism has been amply validated by its intellectual fruits (see the cited network flow application as one example, or the Arora, Hazan, and Kale reference).