Then Omega correctly predicts that you wouldn’t have paid if the coin had come up the other way, and punishes you.
Note: I am using the word “correct” in the sense that you have literally just told us that you wouldn’t have paid if the coin had come up the other way, and it makes no sense to claim anything about “that case regarding the other possibility for the coin is just a hypothetical” since the entire thing being discussed is a hypothetical.
In more detail:
Within the outer hypothetical of this scenario happening at all, Omega’s prediction about the coin-alternative hypothetical is a fact (not a hypothetical) that you are not aware of, but can predict with very high success rate. It is very highly correlated with the output of your decision process, though not caused by the output of your decision process. Both the prediction and the output have a common cause. If your decision process is anywhere near as legible (to Omega) as you state it to be, and results in the output you state, then it will result in you being punished, and this punishment should be highly predictable to you in advance.
However, you have stated that you do not predict punishment, so there is something wrong with your decision process.
However, you have stated that you do not predict punishment, so there is something wrong with your decision process.
Or perhaps with my understanding of the original problem, or its wording. At this point I am not clear who knows what when, and who gets punished under what circumstances.
Honestly, I’ve probably made it more confusing by editing the wording as I go. One thing that might make it easier is the dot points I’ve now added in my post that describe the situation step-by-step. I wish I’d thought of including that at the start.
Then Omega correctly predicts that you wouldn’t have paid if the coin had come up the other way, and punishes you.
Note: I am using the word “correct” in the sense that you have literally just told us that you wouldn’t have paid if the coin had come up the other way, and it makes no sense to claim anything about “that case regarding the other possibility for the coin is just a hypothetical” since the entire thing being discussed is a hypothetical.
In more detail:
Within the outer hypothetical of this scenario happening at all, Omega’s prediction about the coin-alternative hypothetical is a fact (not a hypothetical) that you are not aware of, but can predict with very high success rate. It is very highly correlated with the output of your decision process, though not caused by the output of your decision process. Both the prediction and the output have a common cause. If your decision process is anywhere near as legible (to Omega) as you state it to be, and results in the output you state, then it will result in you being punished, and this punishment should be highly predictable to you in advance.
However, you have stated that you do not predict punishment, so there is something wrong with your decision process.
Or perhaps with my understanding of the original problem, or its wording. At this point I am not clear who knows what when, and who gets punished under what circumstances.
Honestly, I’ve probably made it more confusing by editing the wording as I go. One thing that might make it easier is the dot points I’ve now added in my post that describe the situation step-by-step. I wish I’d thought of including that at the start.