This was fascinating. Thanks for taking the time to write it. I agree with the vast majority of what you wrote, although I don’t think it actually applies to what I was trying to do in this post. I don’t disagree that a full-Bayesian finds this whole thing a bit trivial, but I don’t believe people are fully Bayesian (to the extent they know their utility function) and therefore I think coming up with heuristics is valuable to help them think about things.
So, similarly, I see the Peters justification of Kelly as ultimately just a fancy way of saying that taking the logarithm makes the math nice. You’re leaning on that argument to a large extent, although you also cite some other properties which I have no beef with.
I don’t really think of it as much as an “argument”. I’m not trying to “prove” Kelly criterion. I’m trying to help people get some intuition for where it might come from and some other reasons to consider it if they aren’t utility maximising.
It’s interesting to me that you brought up the exponential St Petersburg paradox, since MacLean, Thorpe, Ziemba claim that Kelly criterion can also handle it although I personally haven’t gone through the math.
Yeah, in retrospect it was a bit straw of me to argue the pure bayesian perspective like I did (I think I was just interested in the pure-bayes response, not thinking hard about what I was trying to argue there).
So, similarly, I see the Peters justification of Kelly as ultimately just a fancy way of saying that taking the logarithm makes the math nice. You’re leaning on that argument to a large extent, although you also cite some other properties which I have no beef with.
I don’t really think of it as much as an “argument”. I’m not trying to “prove” Kelly criterion.
I’m surprised at that. Your post read to me as endorsing Peters’ argument. (Although you did emphasize that you were not trying to say that Kelly was the one true rule.)
Hm. I guess I should work harder on articulating what position I would argue for wrt Kelly. I basically think there exist good heuristic arguments for Kelly, but people often confuse them for more objective than they are (either in an unsophisticated way, like reading standard arguments for Kelly and thinking they’re stronger than they are, or in a sophisticated way, like Peters’ explicit attempt to rewrite the whole foundation of decision theory). Which leads me to reflexively snipe at people who appear to be arguing for Kelly, unless they clearly distinguish themselves from the wrong arguments.
I’m very interested in your potential post on corrections to Kelly.
This was fascinating. Thanks for taking the time to write it. I agree with the vast majority of what you wrote, although I don’t think it actually applies to what I was trying to do in this post. I don’t disagree that a full-Bayesian finds this whole thing a bit trivial, but I don’t believe people are fully Bayesian (to the extent they know their utility function) and therefore I think coming up with heuristics is valuable to help them think about things.
I don’t really think of it as much as an “argument”. I’m not trying to “prove” Kelly criterion. I’m trying to help people get some intuition for where it might come from and some other reasons to consider it if they aren’t utility maximising.
It’s interesting to me that you brought up the exponential St Petersburg paradox, since MacLean, Thorpe, Ziemba claim that Kelly criterion can also handle it although I personally haven’t gone through the math.
Yeah, in retrospect it was a bit straw of me to argue the pure bayesian perspective like I did (I think I was just interested in the pure-bayes response, not thinking hard about what I was trying to argue there).
I’m surprised at that. Your post read to me as endorsing Peters’ argument. (Although you did emphasize that you were not trying to say that Kelly was the one true rule.)
Hm. I guess I should work harder on articulating what position I would argue for wrt Kelly. I basically think there exist good heuristic arguments for Kelly, but people often confuse them for more objective than they are (either in an unsophisticated way, like reading standard arguments for Kelly and thinking they’re stronger than they are, or in a sophisticated way, like Peters’ explicit attempt to rewrite the whole foundation of decision theory). Which leads me to reflexively snipe at people who appear to be arguing for Kelly, unless they clearly distinguish themselves from the wrong arguments.
I’m very interested in your potential post on corrections to Kelly.