I appreciated that you posted this, and I think your further proposed post(s) sound good, too!
To my personal taste, my main disappointment when reading the post was that you didn’t expand this section more:
Utilities and repeated bets are two sides of the same coin
I think this is fairly clear—“The time interpretation of expected utility theory” (Peters, Adamou) prove this. I don’t want to say too much more about this. This section is mostly to acknowledge that:
Yes, Kelly is maximising log utility
No, it doesn’t matter which way you think about this
Yes, I do think thinking in the repeated bets framework is more useful
But that’s a perfectly reasonable choice given (a) writing time constraints, (b) time constraints of readers. You probably shouldn’t feel pressured to expand arguments out more as opposed to writing up rough thoughts with pointers to the info.
Speaking of which, I appreciated all the references you included!
Yeah, I think I’m about to write a reply to your massive comment, but I think I’m getting closer to understanding. I think what I really need to do is write my “Kelly is Black-Scholes for utility” post.
I think that (roughly) this post isn’t aimed at someone who has already decided what their utility is. Most of the examples you didn’t like / saw as non-sequitor were explicitly given to help people think about their utility.
I think that (roughly) this post isn’t aimed at someone who has already decided what their utility is. Most of the examples you didn’t like / saw as non-sequitor were explicitly given to help people think about their utility.
Ah, I suspect this is a mis-reading of my intention. For a good portion of my long response, I was speaking from the perspective of a standard Bayesian. Standard Bayesians have already decided what their utility is. I didn’t intend that part as my “real response”. Indeed, I intended some of it to sound a bit absurd. However, a lotta folks round here are real fond of Bayes, so articulating “the bayesian response” seems relevant.
If you’d wanted to forestall that particular response, in writing the piece, I suppose you could have been more explicit about which arguments are Bayesian, and which are explicitly anti-Bayesian (IE Peters), and where you fall wrt accepting Bayesian / anti-Bayesian assumptions. Partly I thought you might be pretty Bayesian and would take “Bayesians wouldn’t accept this argument” pretty seriously. (Although I also had probability on you being pretty anti-Bayesian.)
I appreciated that you posted this, and I think your further proposed post(s) sound good, too!
To my personal taste, my main disappointment when reading the post was that you didn’t expand this section more:
But that’s a perfectly reasonable choice given (a) writing time constraints, (b) time constraints of readers. You probably shouldn’t feel pressured to expand arguments out more as opposed to writing up rough thoughts with pointers to the info.
Speaking of which, I appreciated all the references you included!
Yeah, I think I’m about to write a reply to your massive comment, but I think I’m getting closer to understanding. I think what I really need to do is write my “Kelly is Black-Scholes for utility” post.
I think that (roughly) this post isn’t aimed at someone who has already decided what their utility is. Most of the examples you didn’t like / saw as non-sequitor were explicitly given to help people think about their utility.
Ah, I suspect this is a mis-reading of my intention. For a good portion of my long response, I was speaking from the perspective of a standard Bayesian. Standard Bayesians have already decided what their utility is. I didn’t intend that part as my “real response”. Indeed, I intended some of it to sound a bit absurd. However, a lotta folks round here are real fond of Bayes, so articulating “the bayesian response” seems relevant.
If you’d wanted to forestall that particular response, in writing the piece, I suppose you could have been more explicit about which arguments are Bayesian, and which are explicitly anti-Bayesian (IE Peters), and where you fall wrt accepting Bayesian / anti-Bayesian assumptions. Partly I thought you might be pretty Bayesian and would take “Bayesians wouldn’t accept this argument” pretty seriously. (Although I also had probability on you being pretty anti-Bayesian.)