Is Omega meant to be immune to the Halting Problem here? (Your own strategy could conceivably depend on trying to predict what Omega would do under some circumstances.) Or are you supposed to be an imperfect reasoner (which may be true in real life, but isn’t normally assumed to be true in these hypothetical scenarios)?
Is Omega meant to be immune to the Halting Problem here?
Why do you think this might be an issue? Can’t we just get around this by giving you a limited amount of time to decide before Omega counts it as you rejecting the offer?
Giving you a limited amount to decide, where that limited amount of time means that you can’t use some lines of reasoning, means that the question is now “what should an imperfect reasoner do when faced with Omega”. The answer to this question 1) depends on the details of the imperfect reasoning and 2) leads to rather less insight on the main question.
Is Omega meant to be immune to the Halting Problem here? (Your own strategy could conceivably depend on trying to predict what Omega would do under some circumstances.) Or are you supposed to be an imperfect reasoner (which may be true in real life, but isn’t normally assumed to be true in these hypothetical scenarios)?
Why do you think this might be an issue? Can’t we just get around this by giving you a limited amount of time to decide before Omega counts it as you rejecting the offer?
Giving you a limited amount to decide, where that limited amount of time means that you can’t use some lines of reasoning, means that the question is now “what should an imperfect reasoner do when faced with Omega”. The answer to this question 1) depends on the details of the imperfect reasoning and 2) leads to rather less insight on the main question.