Oh, you just apply different ergodic transformations to different lotteries, of course.
Also, beware that besides this wrong example, the linked paper contains other basic misconceptions about EE, like for example the claim that EE is equivalent to log utility.
You have to apply different transformations to different lotteries, because EE requires that all lotteries be transformed such that the result is ergodic. There is no single transformation function that can make a multiplicative lottery ergodic while also making an additive lottery ergodic.
the linked paper contains other basic misconceptions about EE, like for example the claim that EE is equivalent to log utility.
It does not make that claim. The claim was that there are multiple transformation functions that can make multiplicative bets ergodic, but in practice, EE proponents always use the logarithm function, which produces a decision theory that’s equivalent to log utility for the special case of multiplicative bets.
EE isn’t VNM because it violates completeness—there are lotteries that can’t be compared to each other. An example (from here):
There is no single transformation function that makes both of these lotteries ergodic, so EE has no way of saying which is better.
I’m not sure whether EE violates independence; like you, I’m not convinced, but I’d have to think about it more to say with confidence.
Oh, you just apply different ergodic transformations to different lotteries, of course.
Also, beware that besides this wrong example, the linked paper contains other basic misconceptions about EE, like for example the claim that EE is equivalent to log utility.
You have to apply different transformations to different lotteries, because EE requires that all lotteries be transformed such that the result is ergodic. There is no single transformation function that can make a multiplicative lottery ergodic while also making an additive lottery ergodic.
It does not make that claim. The claim was that there are multiple transformation functions that can make multiplicative bets ergodic, but in practice, EE proponents always use the logarithm function, which produces a decision theory that’s equivalent to log utility for the special case of multiplicative bets.