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.
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.