You note that expected utility with a risk-averse utility function is sufficient to make appropriate choices [in those particular scenarios].
This is a slight tangent, but I’m curious to what extent you think people actually follow something that approximates this utility function in real life? It seems like some gamblers instinctively use a strategy of this nature (e.g. playing with house money) or explicitly run the numbers (e.g. the Kelly criterion). And I doubt that anyone is dumb enough to keep betting their entire bankroll on a positive EV bet until they inevitably go bust.
But in other cases (like retirement planning, as you mentioned) a lot of people really do seem to make the mistake of relying on ensemble-average probabilities. Some of them will get burned, with much more serious consequences than merely making a silly bet at the casino.
I guess what I’m asking is: even if Peters et al are wrong about expected utility, do you think they’re right about the dangers of failing to understand ergodicity?
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.)
Thanks for taking the time to delve into this!
You note that expected utility with a risk-averse utility function is sufficient to make appropriate choices [in those particular scenarios].
This is a slight tangent, but I’m curious to what extent you think people actually follow something that approximates this utility function in real life? It seems like some gamblers instinctively use a strategy of this nature (e.g. playing with house money) or explicitly run the numbers (e.g. the Kelly criterion). And I doubt that anyone is dumb enough to keep betting their entire bankroll on a positive EV bet until they inevitably go bust.
But in other cases (like retirement planning, as you mentioned) a lot of people really do seem to make the mistake of relying on ensemble-average probabilities. Some of them will get burned, with much more serious consequences than merely making a silly bet at the casino.
I guess what I’m asking is: 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.)