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jsteinhardt comments on Unconditionally Convergent Expected Utility - Less Wrong Discussion
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Comments (32)
Can you clarify what you mean by "this idea"?
Also, doesn't the set of "possible lotteries" have to be the space of lotteries about which VNM can be proved? Probably there are multiple such spaces, but I'm not sure what conditions they have to satisfy. Also, since utilities don't come until after we've chosen a space of lotteries, we can't define the space of lotteries to be "those for which expected utility converges", so I'm not quite sure what you are looking for.
Using priors that allow for unconditionally convergent expected utility.
I don't understand what you mean. The set I'm using is the largest possible set for which all of those axioms are true. If I use one with utility that increases/decreases without limit, axiom 3 (along with 3') is false. If I use one with utility that doesn't converge unconditionally, axiom 2 is false.