I think you avoid any contradiction if you reject Weak Dominance but accept a finite version of Dominance. For example, in that case you can simply declare all lotteries with infinite support to be incomparable to each other or to any finite lottery.
If you furthermore require your preferences to be complete, even when asking about infinite lotteries, such that either A>B or A>B or A=B, then I suspect you are back in trouble.
But if you just restrict preferences to finite lotteries you are fine and can compare them with expected value.
Yeah, maybe just truncating off finitely many summands in an infinite lottery induces constraints that force your examples to have infinite value? Maybe you can have complete hyperreal-valued preferences and finite dominance...?
I think you avoid any contradiction if you reject Weak Dominance but accept a finite version of Dominance. For example, in that case you can simply declare all lotteries with infinite support to be incomparable to each other or to any finite lottery.
If you furthermore require your preferences to be complete, even when asking about infinite lotteries, such that either A>B or A>B or A=B, then I suspect you are back in trouble.
But if you just restrict preferences to finite lotteries you are fine and can compare them with expected value.
Yeah, maybe just truncating off finitely many summands in an infinite lottery induces constraints that force your examples to have infinite value? Maybe you can have complete hyperreal-valued preferences and finite dominance...?