What you’re missing is the F in FDT: the agent is assumed to have a function that maps their available information to a decision. In a note-less scenario, every possible agent has the same information available, and so there are only two possible functions: one that maps to Left, and one that maps to Right. FDT then says that Left performs better.
Once you introduce the possibility of a note, there are now (at least) three values in the domain: no note, a note saying the prediction was Left, and a note saying the prediction was Right. MacAskill assumed that this doesn’t change the FDT decision, but of course it does: there are now at least 8 (and possibly infinitely many) such functions to compare, not just 2, and unstated distributions over the mapping between inputs and outputs. In almost all of the distributions, FDT will in these new and different scenarios recommend picking Right.
What you’re missing is the F in FDT: the agent is assumed to have a function that maps their available information to a decision. In a note-less scenario, every possible agent has the same information available, and so there are only two possible functions: one that maps to Left, and one that maps to Right. FDT then says that Left performs better.
Once you introduce the possibility of a note, there are now (at least) three values in the domain: no note, a note saying the prediction was Left, and a note saying the prediction was Right. MacAskill assumed that this doesn’t change the FDT decision, but of course it does: there are now at least 8 (and possibly infinitely many) such functions to compare, not just 2, and unstated distributions over the mapping between inputs and outputs. In almost all of the distributions, FDT will in these new and different scenarios recommend picking Right.