Omega, a perfect predictor, flips a coin. If if comes up heads, Omega asks you for $100, then pays you $10,000 if it predict you would have paid if it had come up tails. If it comes up tails, Omega asks you for $100, then pays you $10,000 if it predicts you would have paid if it had come up heads
Having a bit of trouble understanding the setup, maybe it can be framed in a way that avoids confusofactuals.
How about “Omega knows whether you would pay in the counterfactual mugging setup if told that you had lost and will reward you for paying if you lose, but you don’t know that you would get rewarded once you pay up”. Is there anything I have missed?
If my understanding is correct, then those who would pay gain either $10,000 or $9,900, and those who would not pay gain either $10,000 or nothing, depending on the coin flip. So, in this setup a payer’s expected gain ($9,950) is higher than a non-payer’s ($5,000).
Note that your formulation has a bunch of superfluous stipulations. Omega is a perfect predictor, so you may as well just get informed of the results and given $10,000, $9,900 or nothing. The only difference is emotional, not logical. For example:
You are the kind of person who would pay $100 in the counterfactual mugging loss, and you did, sadly, lose, so here is your $9,900 reward for being such a good boy. Have a good day!
“How about “Omega knows whether you would pay in the counterfactual mugging setup if told that you had lost and will reward you for paying if you lose, but you don’t know that you would get rewarded once you pay up”. Is there anything I have missed?”—you aren’t told that you “lost” as there is no losing coin flip in this scenario since it is symmetric. You are told which way the coin came up. Anyway, I updated the post to clarify this
Having a bit of trouble understanding the setup, maybe it can be framed in a way that avoids confusofactuals.
How about “Omega knows whether you would pay in the counterfactual mugging setup if told that you had lost and will reward you for paying if you lose, but you don’t know that you would get rewarded once you pay up”. Is there anything I have missed?
If my understanding is correct, then those who would pay gain either $10,000 or $9,900, and those who would not pay gain either $10,000 or nothing, depending on the coin flip. So, in this setup a payer’s expected gain ($9,950) is higher than a non-payer’s ($5,000).
Note that your formulation has a bunch of superfluous stipulations. Omega is a perfect predictor, so you may as well just get informed of the results and given $10,000, $9,900 or nothing. The only difference is emotional, not logical. For example:
“How about “Omega knows whether you would pay in the counterfactual mugging setup if told that you had lost and will reward you for paying if you lose, but you don’t know that you would get rewarded once you pay up”. Is there anything I have missed?”—you aren’t told that you “lost” as there is no losing coin flip in this scenario since it is symmetric. You are told which way the coin came up. Anyway, I updated the post to clarify this