Under ordinary conditions, it’s pretty safe to argue “such and such with probability 1, therefore, it’s safe to pretend such-and-such”. But this happens to be a case where doing so makes us greatly diverge from the Bayesian analysis—ignoring the “most important” worlds from a pure expectation-maximization perspective (IE the ones where we repeatedly win bets, amassing huge sums).
So I’m very against sweeping that particular part of the reasoning under the rug. It’s a reasonable argument, it’s just one that imho should come equipped with big warning lights saying “NOTE: THIS IS A SEVERELY NON-BAYESIAN STEP IN THE REASONING. DO NOT CONFUSE THIS WITH EXPECTATION MAXIMIZATION.”
Instead, you simply said:
To maximize that, we maximize expected log return each timestep, which is the Kelly rule.
which, to my eye, doesn’t provide any warning to the reader. I just really think this kind of argument should be explicit about maximizing modal/median/any-fixed-quantile rather than the more common expectation maximization. Because people should be aware if one of their ideas about rational agency is based on mode/median/quantile maximization rather than expectation maximization.
Under ordinary conditions, it’s pretty safe to argue “such and such with probability 1, therefore, it’s safe to pretend such-and-such”. But this happens to be a case where doing so makes us greatly diverge from the Bayesian analysis—ignoring the “most important” worlds from a pure expectation-maximization perspective (IE the ones where we repeatedly win bets, amassing huge sums).
So I’m very against sweeping that particular part of the reasoning under the rug. It’s a reasonable argument, it’s just one that imho should come equipped with big warning lights saying “NOTE: THIS IS A SEVERELY NON-BAYESIAN STEP IN THE REASONING. DO NOT CONFUSE THIS WITH EXPECTATION MAXIMIZATION.”
Instead, you simply said:
which, to my eye, doesn’t provide any warning to the reader. I just really think this kind of argument should be explicit about maximizing modal/median/any-fixed-quantile rather than the more common expectation maximization. Because people should be aware if one of their ideas about rational agency is based on mode/median/quantile maximization rather than expectation maximization.
Ok, I buy that.