After a good night’s sleep, here are some more thoughts:
the idea is that you pay up because you feel obligated to your counterfactual self.
To feel obligated to my counterfactual self, which exists only in the “mind” of Omega, and not feel obligated to Omega doesn’t make any sense to me.
Your additional assumptions about Omega destroy the utility that the $100 had—in the original version, $100 is $100 to both me and Omega, but in your version it is nothing to Omega. Your amended version of the problem amounts to “would I throw $100 into an incinerator on the basis of some thought experiment”, and that is clearly not even a zero-sum game if you consider the whole system—the original problem is zero-sum, and that gives me more freedom of choice.
After a good night’s sleep, here are some more thoughts:
To feel obligated to my counterfactual self, which exists only in the “mind” of Omega, and not feel obligated to Omega doesn’t make any sense to me.
Your additional assumptions about Omega destroy the utility that the $100 had—in the original version, $100 is $100 to both me and Omega, but in your version it is nothing to Omega. Your amended version of the problem amounts to “would I throw $100 into an incinerator on the basis of some thought experiment”, and that is clearly not even a zero-sum game if you consider the whole system—the original problem is zero-sum, and that gives me more freedom of choice.