Well, sure, by mangling enough the events you can re-establish the axioms...Of course, by splitting the events like that, you’ll reestablish independence—but by showing the need to mangle choices to make fit the axioms, you in fact have shown the axioms don’t work in the general case, when the choices you’re given are not independent, as it often is in real life.
‘If I write out my arithmetic like “one plus two”, your calculator can’t handle it! Proving that arithmetic doesn’t work in the general case. Sure, you can mangle these words into these things you call numbers and symbols like “1+2″, but often in real life we don’t use them.’
Hrm, could you try to steelman instead of strawmaning my position ?
It’s not just a matter of formulation or translating words to symbols. Having to split the choices offered in the real world into an undefined number of virtual choices is not just a switch of notation. Real world choices have far-fetched consequences, and having to split apart all possible interactions between those choices can easily lead to combinatorial explosion of possible choices. benelliott split my choices into 2, but he could have split them into much more : different level of preparation of the trip, buying or not a laptop by myself, …
If it means that the a VNM-based theory can’t handle directly real-life choices without having to convert them into a different set of choices, which can be much bigger than the real-life choices, well, that’s something significant that you can’t just hand-wave with ill-placed irony, and the details of the conversion process have to be part of the decision theory.
Hrm, could you try to steelman instead of strawmaning my position ?
Steelman yourself. I took your quote and replaced it with an isomorphic version; it’s not my problem if it looks even more transparently irrelevant or wrong.
If it means that the a VNM-based theory can’t handle directly real-life choices without having to convert them into a different set of choices, which can be much bigger than the real-life choices, well, that’s something significant that you can’t just hand-wave with ill-placed irony, and the details of the conversion process have to be part of the decision theory.
Yes, it is significant, but it’s along the lines of “most (optimization) problems are in complexity classes higher than P” or “AIXI is uncomputable”. It doesn’t mean that the axioms or proofs are false; it just means that, yet again, as always, we need to make trade-offs and approximations.
‘If I write out my arithmetic like “one plus two”, your calculator can’t handle it! Proving that arithmetic doesn’t work in the general case. Sure, you can mangle these words into these things you call numbers and symbols like “1+2″, but often in real life we don’t use them.’
Hrm, could you try to steelman instead of strawmaning my position ?
It’s not just a matter of formulation or translating words to symbols. Having to split the choices offered in the real world into an undefined number of virtual choices is not just a switch of notation. Real world choices have far-fetched consequences, and having to split apart all possible interactions between those choices can easily lead to combinatorial explosion of possible choices. benelliott split my choices into 2, but he could have split them into much more : different level of preparation of the trip, buying or not a laptop by myself, …
If it means that the a VNM-based theory can’t handle directly real-life choices without having to convert them into a different set of choices, which can be much bigger than the real-life choices, well, that’s something significant that you can’t just hand-wave with ill-placed irony, and the details of the conversion process have to be part of the decision theory.
Steelman yourself. I took your quote and replaced it with an isomorphic version; it’s not my problem if it looks even more transparently irrelevant or wrong.
Yes, it is significant, but it’s along the lines of “most (optimization) problems are in complexity classes higher than P” or “AIXI is uncomputable”. It doesn’t mean that the axioms or proofs are false; it just means that, yet again, as always, we need to make trade-offs and approximations.