I probably don’t have time to answer to this in detail. The way I see you could understand this is to imaging a completely different dynamic, neither multiplicative nor additive, something weirder, like for example square root or raising to power of 2. For each of that dynamic, EE will give different answers, because ergodic mapping is different for each and also—sometimes—dramatically different from log utility, or linear utility.
But I don’t think EE would give different answers! EE would give the answer that would maximise the time-averaged geometric growth rate. That would be the same answer that would maximise the expected final log wealth after a long series of identical decisions.
So yes, what you say is exactly the misconception about EE. EE will give different answers for each different dynamic, because time-average is calculated differently for each dynamic. Please see for example section 6.6. in the book on EE.
I probably don’t have time to answer to this in detail. The way I see you could understand this is to imaging a completely different dynamic, neither multiplicative nor additive, something weirder, like for example square root or raising to power of 2. For each of that dynamic, EE will give different answers, because ergodic mapping is different for each and also—sometimes—dramatically different from log utility, or linear utility.
But I don’t think EE would give different answers! EE would give the answer that would maximise the time-averaged geometric growth rate. That would be the same answer that would maximise the expected final log wealth after a long series of identical decisions.
So yes, what you say is exactly the misconception about EE. EE will give different answers for each different dynamic, because time-average is calculated differently for each dynamic. Please see for example section 6.6. in the book on EE.