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.
My first diagram is scenario C and my second is scenario B. In the first diagram there is no (ETA: causal) dependence of the final mark on exam performance. I think pallas’ intended scenario was more likely to be B: the mark does (ETA: causally) depend on exam performance and has been predicted. Since in B the mark depends on final performance it is necessary to study and take the exam.
In the real world, where teachers do not possess Omega’s magic powers, teachers may very well be able to predict pretty much how their students will do. For that matter, the students themselves can predict how they will do, which transforms the problem into the very ordinary, non-magical one I gave at the end of my comment. If you know how well you will do on the exam, and want to do well on it, should you (i.e. is it the correct decision to) put in the work? Or for another example of topical interest, consider the effects of genes on character.
Unless you draw out the causal diagrams, Omega is just magic: an imaginary phenomenon with no moving parts. As has been observed by someone before on LessWrong, any decision theory can be defeated by suitably crafted magic: Omega fills the boxes, or whatever, in the opposite way to whatever your decision theory will conclude. Problems of that sort offer little insight into decision theory.
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.
My first diagram is scenario C and my second is scenario B. In the first diagram there is no (ETA: causal) dependence of the final mark on exam performance. I think pallas’ intended scenario was more likely to be B: the mark does (ETA: causally) depend on exam performance and has been predicted. Since in B the mark depends on final performance it is necessary to study and take the exam.
In the real world, where teachers do not possess Omega’s magic powers, teachers may very well be able to predict pretty much how their students will do. For that matter, the students themselves can predict how they will do, which transforms the problem into the very ordinary, non-magical one I gave at the end of my comment. If you know how well you will do on the exam, and want to do well on it, should you (i.e. is it the correct decision to) put in the work? Or for another example of topical interest, consider the effects of genes on character.
Unless you draw out the causal diagrams, Omega is just magic: an imaginary phenomenon with no moving parts. As has been observed by someone before on LessWrong, any decision theory can be defeated by suitably crafted magic: Omega fills the boxes, or whatever, in the opposite way to whatever your decision theory will conclude. Problems of that sort offer little insight into decision theory.