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.)
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 that the humans can see the defensive potential of this weapon, but the Babyeaters and the Superhappies can't, is a big flaw in the story. The humans sacrificed billions in order to allow the Superhappies to conquer the Babyeaters, but that makes sense only if the Babyeaters can't figure out the same defense that the humans used. Why not?
Also, the Superhappies' approach to negotiation made no game theoretic sense. What they did was, offer a deal to the other side. If they don't accept, impose the deal on them anyway by force. If they do accept, trust that they will carry out the deal without try to cheat. Given these incentives, why would anyone facing a Superhappy in negotiation not accept and then cheat? I don't see any plausible way in which this morality/negotiation strategy could have become a common one in Superhappy society.
Lastly, I note that the Epilogue of the original ending could be named Atonement as well. After being modified by the Superhappies (like how the Confessor was "rescued"?), the humans would now be atoning for having forced their children suffer pain. What does this symmetry tell us, if anything?
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 salary to build a series of hidden doomsday devices around every human colony, and becomes the dictator of humanity through blackmail. Everyone is forced to adopt an utility function of his choosing as their own. With every resource of humanity devoted to the subject, scientists under his direction eventually discover a defense against the supernova weapon, and soon after that, the Babyeaters are conquered, enslaved, and farmed for their crystal brains. Those brains, when extracted and networked in large arrays, turn out to be the cheapest and most efficient computing substrate in the universe. These advantages provide humanity with such a strong competitive edge, that it never again faces an alien that is its match, at least militarily.
Before the universe ends in a big crunch, the Confessed (humanity's eventual name) goes on to colonize more than (10^9)^(10^9) star systems, and to meet and conquer almost as many alien species, but the Superhappy people are never seen again. Their fate becomes one of the most traded futures in the known universe, but those bets will have to remain forever unsettled.
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 powerful that I can easily find the globally optimal course of action for any set of goals I might have, and notice that the optimal course of action often involves repetition of some kind. Why should I retain my desire not to do the same thing over and over again, which was programmed into me by evolution back when minds had a tendency to get stuck in local optimums?
And once I finally came to that realization, I felt less ashamed of values that seemed 'provincial' - but that's another matter.
Eliezer, I wonder if this actually has more to do with your current belief that rationality equals expected utility maximization. For an expected utility maximizer, there is no distinction between 'provincial' and 'universal' values, and certainly no reason to ever feel ashamed of one's values. One just optimizes according to whatever values one happens to have. But as I argued before, human beings are not expected utility maximizers, and I don't see why we should try to emulate them, especially this aspect.
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.