“Hence the information what I will do cannot have been available to the predictor.” If the latter statement is correct, then how can could have “often correctly predicted the choices of other people, many of whom are similar to you, in the particular situation”?
There’s many possible explanations for this data. Let’s say I start my analysis with the model that the predictor is guessing, and my model attaches some prior probability for them guessing right in a single case. I might also have a prior about the likelihood of being lied about the predictor’s success rate, etc. Now I make the observation that I am being told the predictor was right every single time in a row. Based on this incoming data, I can easily update my beliefs about what happened in the previous prediction excercises: I will conclude that (with some credence) the predictor was guessed right in each individual case or that (also with some credence) I am being lied to about their prediction success. This is all very simple Bayesian updating, no problem at all. As long as my prior beliefs assign nonzero credence to the possibility that the predictor guesses right (and I see not reason why that shouldn’t be a possibility), I don’t need to assign any posterior credence to the (physically impossible) assumption that they could actually foretell the actions.
Let’s say I start my analysis with the model that the predictor is guessing, and my model attaches some prior probability for them guessing right in a single case. I might also have a prior about the likelihood of being lied about the predictor’s success rate, etc. Now I make the observation that I am being told the predictor was right every single time in a row. Based on this incoming data, I can easily update my beliefs about what happened in the previous prediction excercises: I will conclude that (with some credence) the predictor was guessed right in each individual case or that (also with some credence) I am being lied to about their prediction success. This is all very simple Bayesian updating, no problem at all.
Right! If I understand your point correctly, given a strong enough prior for the predictor being lucky or deceptive, it would have to be a lot of evidence to change one’s mind, and the evidence would have to be varied. This condition is certainly not satisfied by the original setup. If your extremely confident prior is that foretelling one’s actions is physically impossible, then the lie/luck hypothesis would have to be much more likely than changing your mind about physical impossibility. That makes perfect sense to me.
I guess one would want to simplify the original setup a bit. What if you had full confidence that the predictor is not a trickster? Would you one-box or two-box? To get the physical impossibility out of the way, they do not necessarily have to predict every atom in your body and mind, just observe you (and read your LW posts, maybe) to Sherlock-like make a very accurate conclusion about what you would decide.
Another question: what kind of experiment, in addition to what is in the setup, would change your mind?
There’s many possible explanations for this data. Let’s say I start my analysis with the model that the predictor is guessing, and my model attaches some prior probability for them guessing right in a single case. I might also have a prior about the likelihood of being lied about the predictor’s success rate, etc. Now I make the observation that I am being told the predictor was right every single time in a row. Based on this incoming data, I can easily update my beliefs about what happened in the previous prediction excercises: I will conclude that (with some credence) the predictor was guessed right in each individual case or that (also with some credence) I am being lied to about their prediction success. This is all very simple Bayesian updating, no problem at all. As long as my prior beliefs assign nonzero credence to the possibility that the predictor guesses right (and I see not reason why that shouldn’t be a possibility), I don’t need to assign any posterior credence to the (physically impossible) assumption that they could actually foretell the actions.
Right! If I understand your point correctly, given a strong enough prior for the predictor being lucky or deceptive, it would have to be a lot of evidence to change one’s mind, and the evidence would have to be varied. This condition is certainly not satisfied by the original setup. If your extremely confident prior is that foretelling one’s actions is physically impossible, then the lie/luck hypothesis would have to be much more likely than changing your mind about physical impossibility. That makes perfect sense to me.
I guess one would want to simplify the original setup a bit. What if you had full confidence that the predictor is not a trickster? Would you one-box or two-box? To get the physical impossibility out of the way, they do not necessarily have to predict every atom in your body and mind, just observe you (and read your LW posts, maybe) to Sherlock-like make a very accurate conclusion about what you would decide.
Another question: what kind of experiment, in addition to what is in the setup, would change your mind?