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Will_Sawin comments on Dutch Books and Decision Theory: An Introduction to a Long Conversation - Less Wrong
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Thanks for the revision.
The Will-to-wager assumption feels too strong for me. I would like, for instance, to be able to say "I will wager up to $0.30 on H, or up to $0.60 on ~H. Likewise, I will sell you a wager on H for $0.70 or more, and on ~H for $0.40 or more."
Of course, that's effectively setting up my own Dutch book, but it feels very natural to me to associate uncertainty in an outcome with "gaps" that I don't want to commit to either hypothesis without more data. Then again, I'm a fan of DST, and that's sort of the point.
I would say that the reason for your intuition that uncertainty => gaps (which seems separate from risk-aversion-induced gaps) is that the person on the other end of the bet may have information you don't, and so them offering to bet you counts as Bayesian evidence that the side they're betting on is correct.
However, e.g., a simple computer program can commit to not knowing anything about the world, and solve this problem.