All decision theory problems are simple ones combined with some confusion that a more enlightened mind would see as redundant and isomorphic to the simple.
All decision theory problems are simple ones combined with some confusion that a more enlightened mind would see as redundant and isomorphic to the simple.
I came to appreciate this particular example when it was observed that EDT and CDT both two box (despite this being a bad decision). Usually one or the other gets it right and people at times take their pick from them on a problem by problem basis (some even try to formalise this ‘take your pick’ algorithm). This scenario is in the ballpark of the simplest problem that really sets the decision theories apart.
I don’t understand why two-boxing is a bad decision when 99.9% of two-boxers will have 2 million dollars and 99.9% of the one-boxers will have only 1 million.
I don’t understand why two-boxing is a bad decision when 99.9% of two-boxers will have 2 million dollars and 99.9% of the one-boxers will have only 1 million.
It is a matter of determining what is controlled by the decision procedure of the player or Omega (who is influenced by the player) and what is controlled by arithmetic and the whims of the person choosing which hypothetical problem to talk about. In this case winning or losing the lottery is pure luck while winning or losing with Omega’s game is determined by the player’s decision. While two-boxing can change the evidence of whether you won the lottery it never influences the lottery outcome one way or the other. On the other hand Omega’s choice is directly determined by the player’s decision procedure.
It may be helpful to consider another hypothetical game which has similar difficulties and which I had previously been using for my purposes in the role of ‘Ultimate Newcomb’s Problem’. Consider:
Take Newcomb’s Problem
Add ‘Transparent Boxes’ modification. (This step is optional—the prohibition on factoring makes the process somewhat opaque.)
Include random component. According to some source considered random Omega fills the big box as usual 99.99% of the time but the remaining 0.01% of the time he inverts his procedure.
Posit the problem where the player finds himself staring at an empty big box and a small box with $1,000. Ask him whether or not he takes the small box.
Many people advocate two-boxing in such a situation. I one box. I would expect people who two box in Randomized Transparent Newcomb’s to also two box here for consistency. I would consider it odd for a RTN two-boxer to One box on Ultimate Newcomb’s. In the above scenario I lose. I get $1,000. But I lose $1,000 1 time out of 10,000 and win $1,000,000 the other 9,999 times. Someone who two boxes potentially wins $1,000 up to 9,999 times out of 10,0000 (finding the equilibrium result there gets weird and depends on details in the specification).
Now I may talk of winning 9,999 times out of 10,000 but that can sound hollow when the fact remains that I lose in the only example brought up. Why do I consider it ok to not win in this case? What makes me think it is ok to optimise for different situations to the one that actually happens? Depending on the point of view this is because I don’t attempt to control random or I don’t attempt to control narrative causality. Omega’s behavior I can influence. I cannot influence assumed random sources and if I follow the improbability to the author’s choice of hypothetical then I choose not to optimize for scenarios based on how likely they are to be discussed. It would be a different question if evidence suggested I was living in a physics based on narrative causality where one-in-a-million chances occur nine times out of ten.
So in short, if the lottery doesn’t give me $2M that is because I am unlucky but if Omega doesn’t give me $1M it is because I am a dumbass. The difference between the two is subtle but critically important.
Sorry for the delay to respond, I’ve been busy last couple weeks.
I think you’ve convinced me regarding this. To discuss my own perspective on this, in the past it took me quite a while before I ‘got’ why one-boxing is the right decision in Transparent Newcomb—it was only once I started thinking of decisions as instances of a decision theory/decision procedure that I realized how a “losing” decision may actually be part of what’s a “winning” decision theory overall—and that therefore one-boxing is the correct strategy in Transparent Newcomb.
I guess that in Ultimate Newcomb, one-boxing remains a winning decision theory, though again the winning decision theory is represented in a seemingly ‘losing’ decision. That I failed to get the correct answer here means that though I had understood, I had not really grokked the logic behind this—I behaved too much as if EDT was correct instead.
Thanks for guiding me through this. Much appreciated!
Not always. Some of them are just ill-defined or impossible, combined with some confusion to stop people noticing. (eg, a version of Transparent Newcomb that doesn’t specify what Omega does if a player decides to oppose Omega’s prediction)
All decision theory problems are simple ones combined with some confusion that a more enlightened mind would see as redundant and isomorphic to the simple.
Then again, a more enlightened mind would know whether 1033 is prime.
I came to appreciate this particular example when it was observed that EDT and CDT both two box (despite this being a bad decision). Usually one or the other gets it right and people at times take their pick from them on a problem by problem basis (some even try to formalise this ‘take your pick’ algorithm). This scenario is in the ballpark of the simplest problem that really sets the decision theories apart.
I don’t understand why two-boxing is a bad decision when 99.9% of two-boxers will have 2 million dollars and 99.9% of the one-boxers will have only 1 million.
It is a matter of determining what is controlled by the decision procedure of the player or Omega (who is influenced by the player) and what is controlled by arithmetic and the whims of the person choosing which hypothetical problem to talk about. In this case winning or losing the lottery is pure luck while winning or losing with Omega’s game is determined by the player’s decision. While two-boxing can change the evidence of whether you won the lottery it never influences the lottery outcome one way or the other. On the other hand Omega’s choice is directly determined by the player’s decision procedure.
It may be helpful to consider another hypothetical game which has similar difficulties and which I had previously been using for my purposes in the role of ‘Ultimate Newcomb’s Problem’. Consider:
Take Newcomb’s Problem
Add ‘Transparent Boxes’ modification. (This step is optional—the prohibition on factoring makes the process somewhat opaque.)
Include random component. According to some source considered random Omega fills the big box as usual 99.99% of the time but the remaining 0.01% of the time he inverts his procedure.
Posit the problem where the player finds himself staring at an empty big box and a small box with $1,000. Ask him whether or not he takes the small box.
Many people advocate two-boxing in such a situation. I one box. I would expect people who two box in Randomized Transparent Newcomb’s to also two box here for consistency. I would consider it odd for a RTN two-boxer to One box on Ultimate Newcomb’s. In the above scenario I lose. I get $1,000. But I lose $1,000 1 time out of 10,000 and win $1,000,000 the other 9,999 times. Someone who two boxes potentially wins $1,000 up to 9,999 times out of 10,0000 (finding the equilibrium result there gets weird and depends on details in the specification).
Now I may talk of winning 9,999 times out of 10,000 but that can sound hollow when the fact remains that I lose in the only example brought up. Why do I consider it ok to not win in this case? What makes me think it is ok to optimise for different situations to the one that actually happens? Depending on the point of view this is because I don’t attempt to control random or I don’t attempt to control narrative causality. Omega’s behavior I can influence. I cannot influence assumed random sources and if I follow the improbability to the author’s choice of hypothetical then I choose not to optimize for scenarios based on how likely they are to be discussed. It would be a different question if evidence suggested I was living in a physics based on narrative causality where one-in-a-million chances occur nine times out of ten.
So in short, if the lottery doesn’t give me $2M that is because I am unlucky but if Omega doesn’t give me $1M it is because I am a dumbass. The difference between the two is subtle but critically important.
Sorry for the delay to respond, I’ve been busy last couple weeks.
I think you’ve convinced me regarding this. To discuss my own perspective on this, in the past it took me quite a while before I ‘got’ why one-boxing is the right decision in Transparent Newcomb—it was only once I started thinking of decisions as instances of a decision theory/decision procedure that I realized how a “losing” decision may actually be part of what’s a “winning” decision theory overall—and that therefore one-boxing is the correct strategy in Transparent Newcomb.
I guess that in Ultimate Newcomb, one-boxing remains a winning decision theory, though again the winning decision theory is represented in a seemingly ‘losing’ decision. That I failed to get the correct answer here means that though I had understood, I had not really grokked the logic behind this—I behaved too much as if EDT was correct instead.
Thanks for guiding me through this. Much appreciated!
Not always. Some of them are just ill-defined or impossible, combined with some confusion to stop people noticing. (eg, a version of Transparent Newcomb that doesn’t specify what Omega does if a player decides to oppose Omega’s prediction)