did Predictor include the note in the simulation, or write it later? If there was even a small (say, anything more than 1 in a million) chance that it was written later, the agent should pick Right.
does Predictor always add a note showing the prediction in this scenario?
We can rule out the combination of both together. It is not possible for Predictor to always write a note that honestly records their prediction including the note and still guarantee 10^-24 chance of prediction error. If the note has nontrivial chance of being a lie, then the agent should always pick Right. So to examine the scenario under FDT, we can assume that the note is genuine, in the case where there is any note at all.
So there are at least eight decision functions, one for every combination inputs of “note says Left”, “note says Right”, or “no note”. We have no information about the circumstances in which the predictor leaves a note or not, and this matters!
If the predictor is adversarial to the extent that they are able to be within the bounds of their 10^-24 prediction error, then FDT does indeed say that the agent should pick Left whenever the predictor says “I predicted Right”. A decision function that picks right upon seeing a note saying “I predicted right” would mean that the predictor can force the agent to almost always pick right and pay $100. The predictor can’t force the agent to burn to death by leaving truthful notes with probability more than 10^-24, so this consideration dominates.
However if the predictor is helpful, then FDT says that the agent should only pick Left when they see a note saying that the prediction was Left. This means that the agent never burns to death, and has only about 10^-24 chance of paying $100. Every other decision function means a comparable chance of burning to death, which is very much worse.
Edit: The previous is all meaningless, because I misread the statement on Predictor’s accuracy. FDT does not endorse taking the left box in this scenario as stated.
Can you explain point 1 further, please? It seems to me subjunctive dependence happens regardless of note inclusion, and thus one’s decision theory should left-box in both cases. (I’ll respond to your other points as well.)
If the note was not included in the simulation, then under FDT there is no subjunctive dependence: the output produced by the simulator is for different input than the ones you actually experienced. In the usual FDT analogy, the fact that both you and Predictor are almost certainly using the same type of calculator means nothing if you’re pressing different buttons. We’re told about Predictor’s simulation fidelity, but that doesn’t mean anything if the inputs to the simulation are not the same as reality.
You can work through FDT with the assumption that that a note is with probability p written after simulating you (with fidelity 1 − 10^-24) without a note, and it says that for all but microscopic p you should choose Right. This is a boring scenario and doesn’t illustrate any differences between decision theories, so I didn’t bother to expand on it.
Edit: The previous is all pointless due to misreading the statement about Predictor’s accuracy. FDT recommends taking the Right box in this scenario regardless of whether points 1 and 2 hold.
I should note that my previous comment is all theoretical wankery. In practice, there is no way that I’ll accept any evidence that a predictor has 10^-24 chance of being wrong. I’m going to take the right box.
I won’t even trust that the right box won’t blow up, since the scenario I’ve been kidnapped into has obviously been devised by a sadistic bastard, and I wouldn’t put it past them to put bombs in both boxes (or under the floor) no matter what the alleged predictor supposedly thinks. Just maybe there’s a slightly better chance of surviving by paying the $100.
There are two huge ambiguities in this scenario:did Predictorinclude the notein the simulation, or write it later? If there was even a small (say, anything more than 1 in a million) chance that it was written later, the agent should pick Right.does Predictoralwaysadd a note showing the prediction in this scenario?We can rule out the combination of both together. It is not possible for Predictor to always write a note that honestly records their prediction including the note and still guarantee 10^-24 chance of prediction error. If the note has nontrivial chance of being a lie, then the agent should always pick Right. So to examine the scenario under FDT, we can assume that the note is genuine, in the case where there is any note at all.So there are at least eight decision functions, one for every combination inputs of “note says Left”, “note says Right”, or “no note”. We have no information about the circumstances in which the predictor leaves a note or not, and this matters!If the predictor isadversarialto the extent that they are able to be within the bounds of their 10^-24 prediction error, then FDT does indeed say that the agent should pick Left whenever the predictor says “I predicted Right”. A decision function that picks right upon seeing a note saying “I predicted right” would mean that the predictor can force the agent toalmost alwayspick right and pay $100. The predictor can’t force the agent to burn to death by leaving truthful notes with probability more than 10^-24, so this consideration dominates.However if the predictor ishelpful, then FDT says that the agent should only pick Left when they see a note saying that the prediction was Left. This means that the agentneverburns to death, and has only about 10^-24 chance of paying $100. Every other decision function means a comparable chance of burning to death, which is very much worse.Edit: The previous is all meaningless, because I misread the statement on Predictor’s accuracy. FDT does not endorse taking the left box in this scenario as stated.
Can you explain point 1 further, please? It seems to me subjunctive dependence happens regardless of note inclusion, and thus one’s decision theory should left-box in both cases. (I’ll respond to your other points as well.)
If the note was not included in the simulation, then under FDT there is no subjunctive dependence: the output produced by the simulator is fordifferent inputthan the ones you actually experienced. In the usual FDT analogy, the fact that both you and Predictor are almost certainly using the same type of calculator means nothing if you’re pressing different buttons. We’re told about Predictor’s simulation fidelity, but that doesn’t mean anything if the inputs to the simulation are not the same as reality.You can work through FDT with the assumption that that a note is with probabilitypwritten after simulating you (with fidelity 1 − 10^-24) without a note, and it says that for all but microscopicpyou should choose Right. This is a boring scenario and doesn’t illustrate any differences between decision theories, so I didn’t bother to expand on it.Edit: The previous is all pointless due to misreading the statement about Predictor’s accuracy. FDT recommends taking the Right box in this scenario regardless of whether points 1 and 2 hold.
I should note that my previous comment is all theoretical wankery. In practice, there is no way that I’ll accept any evidence that a predictor has 10^-24 chance of being wrong. I’m going to take the right box.
I won’t even trust that the right box won’t blow up, since the scenario I’ve been kidnapped into has obviously been devised by a sadistic bastard, and I wouldn’t put it past them to put bombs in both boxes (or under the floor) no matter what the alleged predictor supposedly thinks. Just maybe there’s a slightly better chance of surviving by paying the $100.