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.
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.