In both your problems, the seeming paradox comes from failure to recognize that the two agents (one that Omega has simulated and one making the decision) are facing entirely different prior information. Then, nothing requires them to make identical decisions. The second agent can simulate itself having prior information I1 (that the simulated agent has been facing), then infer Omega’s actions, and arrive at the new prior information I2 that is relevant for the decision. And I2 now is independent of which decision the agent would make given I2.
Are you sure that they are facing different prior information? If the sim is a good one, then the TDT agent won’t be able to tell whether it is the sim or not. However, you are right that one solution could be that there are multiple TDT variants who have different information and so can logically separate their decisions.
I mentioned the problems with that in another response here. The biggest problem is that it seriously undermines the attraction and effectiveness of TDT as a decision theory if different instances of TDT are going to find excuses to separate from each other.
In both your problems, the seeming paradox comes from failure to recognize that the two agents (one that Omega has simulated and one making the decision) are facing entirely different prior information. Then, nothing requires them to make identical decisions. The second agent can simulate itself having prior information I1 (that the simulated agent has been facing), then infer Omega’s actions, and arrive at the new prior information I2 that is relevant for the decision. And I2 now is independent of which decision the agent would make given I2.
Are you sure that they are facing different prior information? If the sim is a good one, then the TDT agent won’t be able to tell whether it is the sim or not. However, you are right that one solution could be that there are multiple TDT variants who have different information and so can logically separate their decisions.
I mentioned the problems with that in another response here. The biggest problem is that it seriously undermines the attraction and effectiveness of TDT as a decision theory if different instances of TDT are going to find excuses to separate from each other.