Yes, this is very much correct. It is invalid reasoning to carry out an FDT decision analysis on a different scenario (without the possibility of a note), claim that you should use the result of that on this one (with the note), and then claim that FDT is a bad decision theory as a result.
The possible inclusion of a note and its contents adds an unknown number of bits of information to the input of the function in FDT, which obviously changes the analysis.
The agent would need extraordinarily strong information about when a note appears and the bounds on its probability of truthfulness in order to decide to take the left box under FDT here (and almost certainly not burn to death because the note is almost certainly lying). Otherwise FDT dictates that you must take the right box.
The exact bounds depend upon the conditions under which a note can appear and what its content can be. If they are not specified then you would need to apply some prior distribution, which unless you are an extremely bizarre person with extremely bizarre priors or utility function, will lead to FDT recommending that you take the right box.
Yes, this is very much correct. It is invalid reasoning to carry out an FDT decision analysis on a different scenario (without the possibility of a note), claim that you should use the result of that on this one (with the note), and then claim that FDT is a bad decision theory as a result.
The possible inclusion of a note and its contents adds an unknown number of bits of information to the input of the function in FDT, which obviously changes the analysis.
The agent would need extraordinarily strong information about when a note appears and the bounds on its probability of truthfulness in order to decide to take the left box under FDT here (and almost certainly not burn to death because the note is almost certainly lying). Otherwise FDT dictates that you must take the right box.
The exact bounds depend upon the conditions under which a note can appear and what its content can be. If they are not specified then you would need to apply some prior distribution, which unless you are an extremely bizarre person with extremely bizarre priors or utility function, will lead to FDT recommending that you take the right box.