From quite some time now, I idealized TDT as something that would decide whatever CDT would wish to be able to force itself to decide, if it were warned about that problem in advance. “If I were warned in advance, what would I promise myself to do?”
In the Newcomb problem, CDT would wish to be able to force itself to 1-box, knowing that it would force Omega to give the million.
In the “gimme $100 when we arrive in town or I leave you in this desert to die” problem, CDT would wish to be able to force itself to give the $100 bucks, lest it would have died of thirst.
In the counterfactual mugging, CDT would wish to be able to force itself to give the $1000, as such an advantageous bet would maximize utility.
Now I don’t know…
if this can be easily formalized,
if this is reflectively consistent
if this is actually rational.
I know nothing about the math behind that, but my instincts tell me “yes” to all of the above (which is why I do give Omega the hundred bucks). Surely someone thought of my idealization, then hit some snag?
It’s want to get counterfactually mugged by Omega if and only if you have very high confidence in your model of how Omega works.
It doesn’t feel rational because our brains have very good intuitions about how people work. If a person tried a counterfactual mugging on you, you’d want to refuse. Odds are that sort of proposition out of the blue is merely an attempt to part you from your money, and there’d be no million dollars waiting for you had the coin turned up heads.
Obvious problem with this refinement: suppose you win 3^^^3 units of utility on a heads. You can’t be certain enough that it’s a scam to reject scam attempts. Actually, never mind, you can scale up your credulity at higher and higher reward amounts—after all, there are many more scammers willing to say 3^^^3 than there are entities that can give you 3^^^3 units of utility.
I didn’t intend to solve Pascal’s Mugging. Extremely high pay-off with slightly less extremely odds still doesn’t feel right. But I have the beginning of a solution: the way the story is told (gimme $5 or I torture 3^^^^^3 people for 9^^^^^^^^9 eons), it doesn’t ask you to bet utility on unfathomable odds, but resources. As we have limited resources, the drop in utility is probably sharper than we might think as we give resources up. For instance, would you bet $1000 for $1M at 1⁄2 odds if it were your last? If having no money causes you to starve, suddenly we’re not talking 500 fold return on investment (on average), but betting your very life at 1⁄2 odds for $1M. And your life is worth 5.2 more than that¹ :-). It doesn’t solve everything (replacing “gimme $5” by “kill your light cone” still is a problem), but I’d say its a start: if there is a Lord Outside the Matrix, it means you have a chance to get out of the box and take over, with possibly an even greater pay-off than the original threat. But for that, you probably need your resources.
[1] can’t find the study, and I hesitate between 5.2 and 5.8. On average, of course.
From quite some time now, I idealized TDT as something that would decide whatever CDT would wish to be able to force itself to decide, if it were warned about that problem in advance. “If I were warned in advance, what would I promise myself to do?”
In the Newcomb problem, CDT would wish to be able to force itself to 1-box, knowing that it would force Omega to give the million.
In the “gimme $100 when we arrive in town or I leave you in this desert to die” problem, CDT would wish to be able to force itself to give the $100 bucks, lest it would have died of thirst.
In the counterfactual mugging, CDT would wish to be able to force itself to give the $1000, as such an advantageous bet would maximize utility.
Now I don’t know…
if this can be easily formalized,
if this is reflectively consistent
if this is actually rational.
I know nothing about the math behind that, but my instincts tell me “yes” to all of the above (which is why I do give Omega the hundred bucks). Surely someone thought of my idealization, then hit some snag?
It’s want to get counterfactually mugged by Omega if and only if you have very high confidence in your model of how Omega works.
It doesn’t feel rational because our brains have very good intuitions about how people work. If a person tried a counterfactual mugging on you, you’d want to refuse. Odds are that sort of proposition out of the blue is merely an attempt to part you from your money, and there’d be no million dollars waiting for you had the coin turned up heads.
Obvious problem with this refinement: suppose you win 3^^^3 units of utility on a heads. You can’t be certain enough that it’s a scam to reject scam attempts. Actually, never mind, you can scale up your credulity at higher and higher reward amounts—after all, there are many more scammers willing to say 3^^^3 than there are entities that can give you 3^^^3 units of utility.
Yes.
Yes.
I didn’t intend to solve Pascal’s Mugging. Extremely high pay-off with slightly less extremely odds still doesn’t feel right. But I have the beginning of a solution: the way the story is told (gimme $5 or I torture 3^^^^^3 people for 9^^^^^^^^9 eons), it doesn’t ask you to bet utility on unfathomable odds, but resources. As we have limited resources, the drop in utility is probably sharper than we might think as we give resources up. For instance, would you bet $1000 for $1M at 1⁄2 odds if it were your last? If having no money causes you to starve, suddenly we’re not talking 500 fold return on investment (on average), but betting your very life at 1⁄2 odds for $1M. And your life is worth 5.2 more than that¹ :-). It doesn’t solve everything (replacing “gimme $5” by “kill your light cone” still is a problem), but I’d say its a start: if there is a Lord Outside the Matrix, it means you have a chance to get out of the box and take over, with possibly an even greater pay-off than the original threat. But for that, you probably need your resources.
[1] can’t find the study, and I hesitate between 5.2 and 5.8. On average, of course.