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.
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.