Using priors that allow for unconditionally convergent expected utility.
Also, doesn’t the set of “possible lotteries” have to be the space of lotteries about which VNM can be proved?
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.
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.