I’ve only skimmed this post so far, so, I’ll need to read it in greater detail. However, I think this is quite related to Nassim Taleb and Ole Peters’ critique of Bayesian decision theory. I’ve left fairly extensive comments there, although I’m afraid I changed my mind a couple of times as I read deeper into the material, and there’s not a nice summary of my final assessment.
I would currently defend the following statements:
From a Bayesian standpoint, Kelly is all about logarithmic utility, and the arguments about repeated bets don’t make very much sense.
From a frequentist standpoint, the arguments about repeated bets make way more sense. Ole Peters is developing a true frequentist decision theory: it used to be that Bayesianism was the only game in town if you wanted your philosophy of statistics to also give you decision theory, but no longer!
I ultimately find Peters’ decision theory unsatisfying. It promises to justify different strategies for different situations (EG logarithmic utility for Kelly-type scenarios), but really, pulls the quantity to be maximized out of thin air (IE the creativity of the practitioner). It’s slight of hand.
Anyway, I’ll read the post more closely, and go further into my critique of Peters if it seems relevant.
Yes—I cited Peters in the post (and stole one of their images). Personally I don’t actually think what they are doing has as much value as they seem to think, although that’s a whole other conversation. I basically think something akin to your third bullet point.
Having read your comments on the other post, I think I understand your critique, and I don’t think there’s much more to be said if you take the utility as axiomatic. However, I guess the larger point I’m trying to make is there are other reasons to care about Kelly other than if you’re a log-utility maximiser. (Several of which you mention in your post)
I’ve only skimmed this post so far, so, I’ll need to read it in greater detail. However, I think this is quite related to Nassim Taleb and Ole Peters’ critique of Bayesian decision theory. I’ve left fairly extensive comments there, although I’m afraid I changed my mind a couple of times as I read deeper into the material, and there’s not a nice summary of my final assessment.
I would currently defend the following statements:
From a Bayesian standpoint, Kelly is all about logarithmic utility, and the arguments about repeated bets don’t make very much sense.
From a frequentist standpoint, the arguments about repeated bets make way more sense. Ole Peters is developing a true frequentist decision theory: it used to be that Bayesianism was the only game in town if you wanted your philosophy of statistics to also give you decision theory, but no longer!
I ultimately find Peters’ decision theory unsatisfying. It promises to justify different strategies for different situations (EG logarithmic utility for Kelly-type scenarios), but really, pulls the quantity to be maximized out of thin air (IE the creativity of the practitioner). It’s slight of hand.
Anyway, I’ll read the post more closely, and go further into my critique of Peters if it seems relevant.
This disagrees with my current understanding, so I’d be interested to hear the reasoning.
Well, here’s my longer response!
Yes—I cited Peters in the post (and stole one of their images). Personally I don’t actually think what they are doing has as much value as they seem to think, although that’s a whole other conversation. I basically think something akin to your third bullet point.
Having read your comments on the other post, I think I understand your critique, and I don’t think there’s much more to be said if you take the utility as axiomatic. However, I guess the larger point I’m trying to make is there are other reasons to care about Kelly other than if you’re a log-utility maximiser. (Several of which you mention in your post)