Well, to my defense you didn’t specify how is Omega 99.9% accurate either. But that does not matter. Let me change the question to fit your framework.
I get this feeling for some “easily read” people. I am about 51% right in both directions of them, and it isn’t correlated with how certain they themselves are about taking the money. Now, suppose you are one of the “easily read” people and you know it. After putting the envelope in your pocket, would you also take the 1000 dollar on the table? Will rejecting it make you richer?
No, I wouldn’t take the money on the table in this case.
I’m easily read, so I already gave off signs of what my decision would turn out to be. You’re not very good at picking them up, but enough that if people in my position take the money then there’s a 49% chance that the envelope contains a million dollars. If they don’t, then there’s a 51% chance that it does.
I’m not going to take $1000 if it is associated with a 2% reduction in the chance of me having a $1000000 in the envelope. On average, that would make me poorer. In the strict local causal sense I would be richer taking the money, but that reasoning is subject to Simpson’s paradox: action Take appears better than Leave for both cases Million and None in the envelope, but is worse when the cases are combined because the weights are not independent. Even a very weak correlation is enough because the pay-offs are so disparate.
I guess that is our disagreement. I would say not taking the money require some serious modification to causal analysis (e.g. retro-causal). You think there doesn’t need to be, it is perfectly resolved by Simpson’s paradox.
Well, to my defense you didn’t specify how is Omega 99.9% accurate either. But that does not matter. Let me change the question to fit your framework.
I get this feeling for some “easily read” people. I am about 51% right in both directions of them, and it isn’t correlated with how certain they themselves are about taking the money. Now, suppose you are one of the “easily read” people and you know it. After putting the envelope in your pocket, would you also take the 1000 dollar on the table? Will rejecting it make you richer?
No, I wouldn’t take the money on the table in this case.
I’m easily read, so I already gave off signs of what my decision would turn out to be. You’re not very good at picking them up, but enough that if people in my position take the money then there’s a 49% chance that the envelope contains a million dollars. If they don’t, then there’s a 51% chance that it does.
I’m not going to take $1000 if it is associated with a 2% reduction in the chance of me having a $1000000 in the envelope. On average, that would make me poorer. In the strict local causal sense I would be richer taking the money, but that reasoning is subject to Simpson’s paradox: action Take appears better than Leave for both cases Million and None in the envelope, but is worse when the cases are combined because the weights are not independent. Even a very weak correlation is enough because the pay-offs are so disparate.
I guess that is our disagreement. I would say not taking the money require some serious modification to causal analysis (e.g. retro-causal). You think there doesn’t need to be, it is perfectly resolved by Simpson’s paradox.