What about the physical process of offering somebody a menu of lotteries consisting only of options that they have seen before? Or a 2-step physical process where first one tells somebody about some set of options, and then presents a menu of lotteries taken only from that set? I can’t think of any example where a rational-seeming preference function doesn’t obey IIA in one of these information-leakage-free physical processes.
Pretentious Penguin
Karma: 108
I think you’re interpreting the word “offer” too literally in the statement of IIA.
Also, any agent who chooses B among {A,B,C} would also choose B among the options {A,B} if presented with them after seeing C. So I think a more illuminating description of your thought experiment is that an agent with limited knowledge has a preference function over lotteries which depends on its knowledge, and that having the linguistic experience of being “offered” a lottery can give the agent more knowledge. So the preference function can change over time as the agent acquires new evidence, but the preference function at any fixed time obeys IIA.
To clarify the last part of your comment, the ratio of the probability of the Great Filter being in front of us to the probability of the Great Filter being behind tool-using intelligent animals should be unchanged by this update, right?
It should be noted that the psychologists and anthropologists in the above tables were not selected based on winning a Nobel prize, nor any prize. On pages 51-52 of The Making of a Scientist Roe writes
For the psychologists the preliminary list was made up by me in consultation, separately, with Dr. E. G. Boring and Dr. David Shakow. We simply went over the membership list of the American Psychological Association and put down everyone we knew to be actively engaged in research and otherwise qualified. This preliminary list was then rated, in the usual fashion, by Dr. Boring, of Harvard University, [...]
and then lists a bunch of other professors involved in rating the list, and “the men who ranked at the top were selected, with some adjustment so as to include representatives of different sorts of psychology.”
(Incidentally, I wonder whether Professor Boring’s lectures lived up to his name.)
Nobel prize winners (especially those in math and sciences) tend to have IQs significantly above the population average.
There is no Nobel prize in math. And the word “especially” would imply that there exists data on the IQs of Nobel laureates in literature and peace which shows a weaker trend than the trend for sciences laureates; has anybody ever managed to convince a bunch of literature Nobel laureates to take IQ tests? I can’t find anything by Googling, and I’m skeptical.
To be clear, the general claim that people who win prestigious STEM awards have above-average IQs is obviously true.
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?
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.
I was assigned this reading for a class once but only skimmed it—now I wish I’d read it more closely!
Okay, so by “wavefunction as a classical mathematical object” you mean a vector in Hilbert space? In that case, what do you mean by the adjective “classical”?
Why do you speak of deterministic, stochastic, and quantum as three options for a fundamental ontology? In the absence of a measurement/collapse postulate, quantum mechanics is a deterministic theory, and with a collapse postulate, it’s a stochastic theory in the sense that the state of the system evolves deterministically except for instantaneous stochastic jumps when “measurements” occur.
Also, what do you mean by “the wavefunction as a classical mathematical object”?
Where could I find the proof that “as quantum amplitude of a piece of the wavefunction goes to zero, the probability that I will ‘find myself’ in that piece also goes to zero” is equivalent to the Born rule?
Neat!
In the linked example, I don’t think “expert consensus” and “groupthink” are two ways to describe the same underlying reality with different emotional valences. Groupthink describes a particular sociological model of how a consensus was reached.