When I translate this sort of situation to anything vaguely real, I find that my response would probably be “please first prove that you’re actually Omega!”
Then if that happened… I would feel super happy to then fork over the $10 <3
Like: it would be it would be freaking awesome to be be counter-factually mugged by Omega and be convinced that I had to then hand over $10 because $10 is totally worth the privilege of talking to a fair god and knowing you’re talking to a fair god!
But the practical question arises: how would anyone really know such a thing?
I’m pretty sure that there is a way for something with hyper-computation to prove to me that it has incredible powers to compute. Factor super big numbers. Solve an NP-complete problem. Whatever.
The part I have trouble with is finding any way to tell demons apart from angels. It seems like it would be easy for someone to prove that they can always predict everything you do before you do it. Angels can do that… but so can demons.
How do you know that the entity is telling the truth about this part: “if it had come up heads, I would have given you 100 dollars (at all, ever, under any circumstances)”.
How does a thing with hyper-computational powers prove that it is benevolent or fair or has any other coherently positive and enduring moral tendencies?
I’ve been failing to come up with any solution to this puzzle for years, but it seems like maybe a more productive approach at this point might be to try to prove the pessimistic version instead.
And when I think of trying to prove the pessimistic version, a formalism of the sort you’ve offered here seems like it might make it possible to state axioms that (1) roughly describe the setup in these motivating stories (with Omega next to a predictable agent, and so on) and (2) allow a normal mathematician to prove from these axioms that a proof of benevolence (from something formally Omega-like to something formally more finite in its powers of reasoning)… is actually just straightforwardly impossible.
Omega and hypercomputational powers isn’t needed, just decent enough prediction about what someone would do. I’ve seen Transparent Newcomb being run on someone before, at a math camp. They were predicted to not take the small extra payoff, and they didn’t. And there was also an instance of acausal vote trading that I managed to pull off a few years ago, and I’ve put someone in a counterfactual mugging sort of scenario where I did pay out due to predicting they’d take the small loss in a nearby possible world. 2⁄3 of those instances were cases where I was specifically picking people that seemed unusually likely to take this sort of thing seriously, and it was predictable what they’d do.
I guess you figure out the entity is telling the truth in roughly the same way you’d figure out a human is telling the truth? Like “they did this a lot against other humans and their prediction record is accurate”.
And no, I don’t think that you’d be able to get from this mathematical framework to proving “a proof of benevolence is impossible”. What the heck would that proof even look like?
What the heck would that proof even look like, indeed. That’s what I haven’t figured out yet.
(On the practical level… I’m pretty sure it would be awesome to interact with a benevolent god and it seems that the thing you’re suggesting is that there are prosaic versions.
One obvious prosaic version of such proximity is a job in finance. The courts and contracts and so on are kind of like Omega, and surely this entity is benevolent? Luck goes well: millions in bonuses. Luck goes bad: you’re laid off. Since of course the system in general is benevolent: surely it would be acceptable to participate? The personal asymmetry in outcomes would make the whole situation potentially nice to be near to.
But then I wonder about that assumption of benevolence and think about Mammon, and I remember The Big Short …and I go back to wondering how Omega offers a finite creature a proof of benevolence.)
The proof of benevolence is a red herring. Just imagine the exact same game happening again and again. Eventually you should become convinced that the game works as advertised.
When I translate this sort of situation to anything vaguely real, I find that my response would probably be “please first prove that you’re actually Omega!”
Then if that happened… I would feel super happy to then fork over the $10 <3
Like: it would be it would be freaking awesome to be be counter-factually mugged by Omega and be convinced that I had to then hand over $10 because $10 is totally worth the privilege of talking to a fair god and knowing you’re talking to a fair god!
But the practical question arises: how would anyone really know such a thing?
I’m pretty sure that there is a way for something with hyper-computation to prove to me that it has incredible powers to compute. Factor super big numbers. Solve an NP-complete problem. Whatever.
The part I have trouble with is finding any way to tell demons apart from angels. It seems like it would be easy for someone to prove that they can always predict everything you do before you do it. Angels can do that… but so can demons.
How do you know that the entity is telling the truth about this part: “if it had come up heads, I would have given you 100 dollars (at all, ever, under any circumstances)”.
How does a thing with hyper-computational powers prove that it is benevolent or fair or has any other coherently positive and enduring moral tendencies?
I’ve been failing to come up with any solution to this puzzle for years, but it seems like maybe a more productive approach at this point might be to try to prove the pessimistic version instead.
And when I think of trying to prove the pessimistic version, a formalism of the sort you’ve offered here seems like it might make it possible to state axioms that (1) roughly describe the setup in these motivating stories (with Omega next to a predictable agent, and so on) and (2) allow a normal mathematician to prove from these axioms that a proof of benevolence (from something formally Omega-like to something formally more finite in its powers of reasoning)… is actually just straightforwardly impossible.
Omega and hypercomputational powers isn’t needed, just decent enough prediction about what someone would do. I’ve seen Transparent Newcomb being run on someone before, at a math camp. They were predicted to not take the small extra payoff, and they didn’t. And there was also an instance of acausal vote trading that I managed to pull off a few years ago, and I’ve put someone in a counterfactual mugging sort of scenario where I did pay out due to predicting they’d take the small loss in a nearby possible world. 2⁄3 of those instances were cases where I was specifically picking people that seemed unusually likely to take this sort of thing seriously, and it was predictable what they’d do.
I guess you figure out the entity is telling the truth in roughly the same way you’d figure out a human is telling the truth? Like “they did this a lot against other humans and their prediction record is accurate”.
And no, I don’t think that you’d be able to get from this mathematical framework to proving “a proof of benevolence is impossible”. What the heck would that proof even look like?
What the heck would that proof even look like, indeed. That’s what I haven’t figured out yet.
(On the practical level… I’m pretty sure it would be awesome to interact with a benevolent god and it seems that the thing you’re suggesting is that there are prosaic versions.
One obvious prosaic version of such proximity is a job in finance. The courts and contracts and so on are kind of like Omega, and surely this entity is benevolent? Luck goes well: millions in bonuses. Luck goes bad: you’re laid off. Since of course the system in general is benevolent: surely it would be acceptable to participate? The personal asymmetry in outcomes would make the whole situation potentially nice to be near to.
But then I wonder about that assumption of benevolence and think about Mammon, and I remember The Big Short …and I go back to wondering how Omega offers a finite creature a proof of benevolence.)
The proof of benevolence is a red herring. Just imagine the exact same game happening again and again. Eventually you should become convinced that the game works as advertised.