I agree with your prescriptive vs descriptive thing, and agree that I was basically making that mistake.
I think the correct position here is something like: expected utility maximization; and also, utility in “these cases” is going to be close to logarithmic. (IE, if you evolve trading strategies in something resembling Kelly’s conditions, you’ll end up with something resembling Kelly agents. And there’s probably some generalization of this which plausibly abstracts aspects of the human condition.)
Ole Peters is trying to re-found decision theory on the basis of this second layer alone. I think this is basically a good instinct:
It’s good to try to firm up this second layer, since just Kelly alone is way too special-case, and we’d like to understand the phenomenon in as much generality as possible.
It’s good to try and make a 1-layer system rather than a 2-layer one, to try and make our principles as unified as possible. The Kelly idea is consistent with our foundation of expectation maximization, sure, but if “realistic” agents systematically avoid some utility functions, that makes expectation maximization a worse descriptive theory. Perhaps there is a better one.
This is similar to the way Solomonoff is a two-layer system: there’s a lower layer of probability theory, and then on top of that, there’s the layer of algorithmic information theory, which tells us to prefer particular priors. In hindsight this should have been “suspicious”; logical induction merges those two layers together, giving a unified framework which gives us (approximately) probability theory and also (approximately) algorithmic information theory, tying them together with a unified bounded-loss notion. (And also implies many new principles which neither probability theory nor algorithmic information theory gave us.)
So although I agree that your descriptive lens is the better one, I think that lens has similar implications.
As for your comments about symmetry—I must admit that I tend to find symmetry arguments to be weak. Maybe you can come up with something cool, but I would tend to predict it’ll be superseded by less symmetry-based alternatives. For one thing, it tends to be a two-layered thing, with symmetry constraints added on top of more basic ideas.
I agree with your prescriptive vs descriptive thing, and agree that I was basically making that mistake.
I think the correct position here is something like: expected utility maximization; and also, utility in “these cases” is going to be close to logarithmic. (IE, if you evolve trading strategies in something resembling Kelly’s conditions, you’ll end up with something resembling Kelly agents. And there’s probably some generalization of this which plausibly abstracts aspects of the human condition.)
But note how piecemeal and fragile this sounds. One layer is the relatively firm expectation-maximization layer. On top of this we add another layer (based on maximization of mode/median/quantile, so that we can ignore things not true with probability 1) which argues for some utility functions in particular.
Ole Peters is trying to re-found decision theory on the basis of this second layer alone. I think this is basically a good instinct:
It’s good to try to firm up this second layer, since just Kelly alone is way too special-case, and we’d like to understand the phenomenon in as much generality as possible.
It’s good to try and make a 1-layer system rather than a 2-layer one, to try and make our principles as unified as possible. The Kelly idea is consistent with our foundation of expectation maximization, sure, but if “realistic” agents systematically avoid some utility functions, that makes expectation maximization a worse descriptive theory. Perhaps there is a better one.
This is similar to the way Solomonoff is a two-layer system: there’s a lower layer of probability theory, and then on top of that, there’s the layer of algorithmic information theory, which tells us to prefer particular priors. In hindsight this should have been “suspicious”; logical induction merges those two layers together, giving a unified framework which gives us (approximately) probability theory and also (approximately) algorithmic information theory, tying them together with a unified bounded-loss notion. (And also implies many new principles which neither probability theory nor algorithmic information theory gave us.)
So although I agree that your descriptive lens is the better one, I think that lens has similar implications.
As for your comments about symmetry—I must admit that I tend to find symmetry arguments to be weak. Maybe you can come up with something cool, but I would tend to predict it’ll be superseded by less symmetry-based alternatives. For one thing, it tends to be a two-layered thing, with symmetry constraints added on top of more basic ideas.