So would it be accurate to say that a preference over lotteries (where each lottery involves only real-valued probabilities) satisfies the axioms of the VNM theorem (except for the Archimedean property) if and only if that preference is equivalent to maximizing the expectation value of a surreal-valued utility function?
Re the parent example, I agree that changing in an expectable way is problematic to rational optimizing, but I think "what kind of agent am I happy about being?" is a distinct question from "what kinds of agents exist among minds in the world?".
If you're on macOS and still want caps lock to be accessible for the rare occasions when you want it, you can use Karabiner-Elements to swap the caps lock key and the escape key.
What is the precise statement for being able to use surreal numbers when we remove the Archimedean axiom? The surreal version of the VNM representation theorem in "Surreal Decisions" (https://arxiv.org/abs/2111.00862) seems to still have a surreal version of the Archimedean axiom.
Re the parent example, I was imagining that the 2-priority utility function for the parent only applied after they already had children, and that their utility function before having children is able to trade off between not having children, having some who live, and having some who die. Anecdotally it seems a lot of new parents experience diachronic inconsistency in their preferences.
It seems to me that the "continuity/Archimedean" property is the least intuitively necessary of the four axioms of the VNM utility theorem. One way of specifying preferences over lotteries that still obeys the other three axioms is assigning to each possible world two real numbers and instead of one, where is a "top priority" and is a "secondary priority". If two lotteries have different , the one with greater is ranked higher, and is used as a tie-breaker. One possible real-world example (with integer-valued for deterministic outcomes) would be a parent whose top priority is minimizing the number of their children who die within the parent's lifetime, with the rest of their utility function being secondary.
I'd be interested in whether there exist any preferences over lotteries quantifying our intuitive understanding of risk aversion while still obeying the other three axioms of the VNM theorem. I spent about an hour trying to construct an example without success, and suspect it might be impossible.
It seems to me that another common and valid reason for insurance is if your utility is a nonlinear function of your wealth, but the insurance company values wealth linearly on the margin. E.g. for life insurance, the marginal value of a dollar for your kids after you die so that they can have food and housing and such is much higher than the marginal value of a dollar paid in premiums while you’re working.
If you wanted to learn that there was a new deadly epidemic in China, you’d have to expose yourself to a lot of content most people would rather not see.
I don't think this claim as written is true. I learned of COVID-19 for the first time from BBC News on New Years' Eve 2019 and followed the course of the pandemic obsessively in January/February on BBC News and some academic website whose name I've forgotten (I think it was affiliated with the University of Washington?) without ever going on 4chan or other similar forums.
Maybe instead narrating posts automatically when published, the poster could be shown a message like “Do you want to narrate this post right now? Once narrated, the audio cannot be changed.” And if they say no then there’s a button they can press to narrate it later (e.g. after editing). And maybe you could charge $1 if people want to change the audio after accepting their one free narration?
quinoa or "raw water" or burnt food or fad diets
What's wrong with quinoa?
Hmmm, I think there's still some linguistic confusion remaining. While we certainly need to invent new mathematics to describe quantum field theory, are you making the stronger claim that there's something "non-native" about the way that wavefunctions in non-relativistic quantum mechanics are described using functional analysis? Especially since a lot of modern functional analysis theory was motivated by quantum mechanics, I don't see how a new branch of math could describe wavefunctions more natively.
The title of this post was effectively clickbait for me, since my primary thought in clicking on it was "I wonder what claim the post will make about the foundations of quantum mechanics", but then I discovered this topic is relegated to a follow-up post. Maybe "Chance is in the map, not the (classical) territory" or "Chance is in the map, not the territory: Part 1" would've been better titles?