But you aren’t supposed to be updating… the essence of UDT, I believe, is that your policy should be set NOW, and NEVER UPDATED.
So… either:
You consider the choice of policy based on the prior where you DIDN’T KNOW whether you’d face Nomega or Omega, and NEVER UPDATE IT (this seems obviously wrong to me: why are you using your old prior instead of your current posterior?).
or
You consider the choice of policy based on the prior where you KNOW that you are facing Omega AND that the coin is tails, in which case paying Omega only loses you money.
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.
But you aren’t supposed to be updating… the essence of UDT, I believe, is that your policy should be set NOW, and NEVER UPDATED.
So… either:
You consider the choice of policy based on the prior where you DIDN’T KNOW whether you’d face Nomega or Omega, and NEVER UPDATE IT (this seems obviously wrong to me: why are you using your old prior instead of your current posterior?). or
You consider the choice of policy based on the prior where you KNOW that you are facing Omega AND that the coin is tails, in which case paying Omega only loses you money.
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.