juramaia-blog asked: "I know I am resurrecting posts from a debate nearly 3 years ago here, sorry" - I'm not sorry, you consistently have new, useful, and correct things to say.

Thanks.  I guess I mostly apologizing to Scott, since those old posts might not reflect his current views, or the way he would phrase them, and anyway I already argued with them back at the time they were posted.

juramaia-blog asked: I still think you're missing why Kelly claims objectivity. It's not that you can hold a growth rate in your hand, it's this statement: "If we compare the fates of two gamblers, however, playing a nonterminating game, the one which uses the value L found above will, with probability one, eventually get ahead and stay ahead of one using any other L." You will almost surely have more of the actual, physical, important stuff eventually.

Ohh, yes, I did miss that and I see the point, thanks.

This actually means it’s sort of an “objective” justification for loss aversion, which is really cool.

On the other hand, we’re still making a judgment as to how we want to value money over time: we only care about getting ahead asymptotically, no matter how long it takes.  IRL, of course people have time preference and do some sort of discounting (exponential, hyperbolic, whatever), in which case it matters how long it takes to get ahead.  This isn’t a problem for Kelly’s paper, which just wants to compute something objective even if it isn’t what any human would care about in practice, but it is a problem for the claim that the Kelly criterion is the one right way to think about the risk-reward tradeoff.

Going back to the original issue I was raising – predictions of objective economic quantities do need to be put through some sort of utility function before we humans can make decisions on the basis of them, and this utility function should see risk vs. reward as a tradeoff, and while it’s cool that “maximize asymptotic growth rate” does that, it still doesn’t capture what you and I actually value.

juramaia-blog asked: The log in the Kelly criterion doesn't come from valuing money logarithmically, it comes from only caring about the amount of money you have as N->infinity. Instead of maximizing E[V_N] and then letting N vary, he wants to maximize E[lim_{N->inf} V_N], but that limit generally diverges so you need to rescale.

I know this, but that re-scaling is equivalent to valuing money logarithmically (at any given time).

Where I disagree with Kelly (in his paper) is that he seems to want a case where a particular quantity (Shannon’s transmission rate) pops out of a calculation that is somehow objective, in that we don’t have to choose some arbitrary utility function, or make some other such value judgment.  And I could buy this if the computation were about the actual physical value of something widely agreed to be important, like E[V_N] at some specific N – yeah, in some sense that implies a “linear utility function,” but you can also think of it as “how much of this actual, physical, important stuff will you have at time N” which feels sufficiently objective to me.

But Kelly chooses this limit, and then needs to rescale, and that introduces a certain arbitrariness – it may well be the only interesting rescaling, but it’s still a non-physical, derived quantity we’ve simply decided to care about (as a value judgment).  You can’t hold a growth rate in your hand, much less a limiting growth rate.