For the School Mark problem, the causal diagram I obtain from the description is one of these:
diagram
or
diagram
For the first of these, the teacher has waived the requirement of actually sitting the exam, and the student needn’t > bother. In the second, the pupil will not get the marks except by studying for and taking the exam. See also the decision problem I describe at the end of this comment.
I think it’s clear that Pallas had the first diagram in mind, and his point was exactly that the rational thing to do is to study despite the fact that the mark has already been written down. I agree with this.
Think of the following three scenarios:
A: No prediction is made and the final grade is determined by the exam performance.
B: A perfect prediction is made and the final grade is determined by the exam performance.
C: A perfect prediction is made and the final grade is based on the prediction.
Clearly, in scenario A the student should study. You are saying that in scenario C, the rational thing to do is not studying. Therefore, you think that the rational decision differs between either A and B, or between B and C. Going from A to B, why should the existence of someone who predicts your decision (without you knowing the prediction!) affect which decision the rational one is? That the final mark is the same in B and C follows from the very definition of a “perfect prediction”. Since each possible decision gives the same final mark in B and C, why should the rational decision differ?
In all three scenarios, the mapping from the set of possible decisions to the set of possible outcomes is identical—and this mapping is arguably all you need to know in order to make the correct decision. ETA: “Possible” here means “subjectively seen as possible”.
By deciding whether or not to learn, you can, from your subjective point of view, “choose” wheter you were determined to learn or not.
The results you quote are very interesting and answer questions I’ve been worrying about for some time. Apologies for bringing up two purely technical inquiries:
Could you provide a reference for the result you quote? You referred to Eq. (34) in Everett’s original paper in another comment, but this doesn’t seem to make the link to the VNM axioms and decision theory.
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That seems wrong to me. There has to be a formulation of the form if the two initially perfectly entangled particles get only slightly entangled with other particles, then quantum teleportation still works with high fidelity / a high probability of success—otherwise quantum teleportation wouldn’t be feasible in reality.