It doesn’t prevent doing different actions in different circumstances, though. That’s not what “updateless” means. It means that you should act as your past self would have precommitted to doing in your situation. Your probability estimate for “I see Omega” should be significantly greater than “I see Omega, and also Nomega is watching and deciding how to act”, so your decision should be mostly determined by Omega, not Nomega. (The Metanomega also applies—there’s a roughly equal chance of Metanomega or Nomega waiting and watching. [Metanomega = Nomega reversed; gives payoff iff predicts you paying.])
I see where I went wrong. I assumed that the impact of one’s response to Omega is limited to the number of worlds in which Omega exists. That is, my reasoning is invalid if (“what I do in scenario X” is meaningful and affects the world even if scenario X never happens). In other words, when one is being counterfactually modeled, which is exactly the topic of discussion.
It doesn’t prevent doing different actions in different circumstances, though. That’s not what “updateless” means. It means that you should act as your past self would have precommitted to doing in your situation. Your probability estimate for “I see Omega” should be significantly greater than “I see Omega, and also Nomega is watching and deciding how to act”, so your decision should be mostly determined by Omega, not Nomega. (The Metanomega also applies—there’s a roughly equal chance of Metanomega or Nomega waiting and watching. [Metanomega = Nomega reversed; gives payoff iff predicts you paying.])
I see where I went wrong. I assumed that the impact of one’s response to Omega is limited to the number of worlds in which Omega exists. That is, my reasoning is invalid if (“what I do in scenario X” is meaningful and affects the world even if scenario X never happens). In other words, when one is being counterfactually modeled, which is exactly the topic of discussion.