Wei_Dai2
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Robin, what is your favorite piece of academic philosophy that argues about values?
Nicholas, our own universe may have an infinite volume, and it's only the speed of light that limits the size of the observable universe. Given that infinite universes are not considered implausible, and starlines are not considered implausible (at least as a fictional device), I find it surprising that you consider starlines that randomly connect a region of size 2^(10^20) to be implausible.
Starlines have to have an average distance of something, right? Why not 2^(10^20)?
Nicholas, suppose Eliezer's fictional universe contains a total of 2^(10^20) star systems, and each starline connects two randomly selected star systems. With a 20 hour doubling speed, the Superhappies, starting with one ship, can explore 2^(t36524/20) random star systems after t years. Let's say the humans are expanding at the same pace. How long will it take, before humans and Superhappies will meet again?
According to the birthday paradox, they will likely meet after each having explored about sqrt(2^(10^20)) = 2^(510^19) star systems, which will take 510^19/(365*24/20) or approximately 10^17 years to accomplish. That should be enough time to get over our attachment to "bodily pain, embarrassment, and romantic troubles", I imagine.
But the tech in the story massively favors the defense, to the point that a defender who is already prepared to fracture his starline network if attacked is almost impossible to conquer (you’d need to advance faster than the defender can send warnings of your attack while maintaining perfect control over every system you’ve captured). So an armed society would have a good chance of being able to cut itself off from even massively superior aliens, while pacifists are vulnerable to surprise attacks from even fairly inferior ones.
I agree, and that's why in my ending humans conquer the Babyeaters only after we develop a defense against the supernova weapon. The fact... (read more)
So, what about the fact that all of humanity now knows about the supernova weapon? How is it going to survive the next few months?
In case it wasn't clear, the premise of my ending is that the Ship's Confessor really was a violent thief and drug dealer from the 21th century, but his "rescue" was only partially successful. He became more rational, but only pretended to accept what became the dominant human morality of this future, patiently biding time his whole life for an opportunity like this.
The Ship's Confessor uses the distraction to anesthetizes everyone except the pilot. He needs the pilot to take command of the starship and to pilot it. The ship stays to observe which star the Superhappy ship came from, then takes off for the nearest Babyeater world. They let the Babyeaters know what happened, and tell them to supernova the star that Superhappies came from at all costs.
When everyone wakes up, the Ship's Confessor convinces the entire crew to erase their memory of the true Alderson's Coupling Constant, ostensibly for the good of humanity. He pretends to do so himself, but doesn't. After the ship returns to human space, he uses his accumulated... (read more)
Eliezer, I see from this example that the Axiom of Independence is related to the notion of dynamic consistency. But, the logical implication goes only one way. That is, the Axiom of Independence implies dynamic consistency, but not vice versa. If we were to replace the Axiom of Independence with some sort of Axiom of Dynamic Consistency, we would no longer be able to derive expected utility theory. (Similarly with dutch book/money pump arguments, there are many ways to avoid them besides being an expected utility maximizer.)
I'm afraid that the Axiom of Independence cannot really be justified as a basic principle of rationality. Von Neumann and Morgenstern probably came up with it because it was mathematically necessary to derive Expected Utility Theory, then they and others tried to justify it afterward because Expected Utility turned out to be such an elegant and useful idea. Has anyone seen Independence proposed as a principle of rationality prior to the invention of Expected Utility Theory?
To expand on my categorization of values a bit more, it seems clear to me that at least some human value do not deserved to be forever etched into the utility function of a singleton. Those caused by idiosyncratic environmental characteristics like taste for salt and sugar, for example. To me, these are simply accidents of history, and I wouldn't hesitate (too much) to modify them away in myself, perhaps to be replaced by more interesting and exotic tastes.
What about reproduction? It's a value that my genes programmed into me for their own purposes, so why should I be obligated to stick with it forever?
Or consider boredom. Eventually I may become so... (read more)
Tim and Tyrrell, do you know the axiomatic derivation of expected utility theory? If you haven't read http://cepa.newschool.edu/het/essays/uncert/vnmaxioms.htm or something equivalent, please read it first.
Yes, if you change the spaces of states and choices, maybe you can encode every possible agent as an utility function, not just those satisfying certain axioms of "rationality" (which I put in quotes because I don't necessarily agree with them), but that would be to miss the entire point of expected utility theory, which is that it is supposed to be a theory of rationality, and is supposed to rule out irrational preferences. That means using state and choice spaces where those axiomatic constraints have real world meaning.
This is fascinating. JW plays C in the last round, even though AA just played D in the next-to-last round. What explains that? Maybe JW's belief in his own heroic story is strong enough to make him sacrifice his self-interest?
Theoretically, of course, utility functions are invariant up to affine transformation, so a utility's absolute sign is not meaningful. But this is not always a good metaphor for real life.
So you're suggesting that real life has some additional structure which is not representable in ordinary game theory formalism? Can you think of an extension to game theory which can represent it? (Mathematically, not just metaphorically.)