even if Peters et al are wrong about expected utility, do you think they’re right about the dangers of failing to understand ergodicity?
Not sure. I can’t tell what additional information, if any, Peters is contributing that you can’t already get from learning about the math of wagers and risk-averse utility functions.
It seems to me like it’s right. So far as I can tell, the “time-average vs ensemble average” argument doesn’t really make sense, but it’s still true that log-wealth maximization is a distinguished risk-averse utility function with especially good properties.
Idealized markets will evolve to contain only Kelly bettors, as other strategies either go bust too often or have sub-optimal growth.
BUT, keep in mind we don’t live in such an idealized market. In reality, it only makes sense to use this argument to conclude that financially savvy people/institutions will be approximate log-wealth maximizers—IE, the people/organizations with a lot of money. Regular people might be nowhere near log-wealth-maximizing, because “going bust” often doesn’t literally mean dying; you can be a failed serial startup founder, because you can crash on friends’/parents’ couches between ventures, work basic jobs when necessary, etc.
More generally, evolved organisms are likely to be approximately log-resource maximizers. I’m less clear on this argument, but the situation seems analogous. It therefore may make sense to suppose that humans are approximate log-resource maximizers.
(I’m not claiming Peters is necessarily adding anything to this analysis.)
Not sure. I can’t tell what additional information, if any, Peters is contributing that you can’t already get from learning about the math of wagers and risk-averse utility functions.
It seems to me like it’s right. So far as I can tell, the “time-average vs ensemble average” argument doesn’t really make sense, but it’s still true that log-wealth maximization is a distinguished risk-averse utility function with especially good properties.
Idealized markets will evolve to contain only Kelly bettors, as other strategies either go bust too often or have sub-optimal growth.
BUT, keep in mind we don’t live in such an idealized market. In reality, it only makes sense to use this argument to conclude that financially savvy people/institutions will be approximate log-wealth maximizers—IE, the people/organizations with a lot of money. Regular people might be nowhere near log-wealth-maximizing, because “going bust” often doesn’t literally mean dying; you can be a failed serial startup founder, because you can crash on friends’/parents’ couches between ventures, work basic jobs when necessary, etc.
More generally, evolved organisms are likely to be approximately log-resource maximizers. I’m less clear on this argument, but the situation seems analogous. It therefore may make sense to suppose that humans are approximate log-resource maximizers.
(I’m not claiming Peters is necessarily adding anything to this analysis.)