by running a simulation of you and seeing what that simulation did.
A simulation of your choice “upon seeing a bomb in the Left box under this scenario”? In that case, the choice to always take the Right box “upon seeing a bomb in the Left box under this scenario” is correct, and what any of the decision theories would recommend. Being in such a situation does necessitate the failure of the predictor, which means you are in a very improbable world, but that is not relevant to your decision in the world you happen to be in (simulated or not).
Or: A simulation of your choice in some different scenario (e.g. not seeing the contents of the boxes)? In that simulation, you would choose some box, but regardless of what that decision would happen to be, you are free to pick the Right box in this scenario, because it is a different scenario. Perhaps you picked Left in the alternative scenario, perhaps the predictor failed; neither is relevant here.
Why would any decision theory ever choose “Left” in this scenario?
A simulation of your choice “upon seeing a bomb in the Left box under this scenario”? In that case, the choice to always take the Right box “upon seeing a bomb in the Left box under this scenario” is correct, and what any of the decision theories would recommend.
Good point. It seems to me Left-boxing is still the right answer though, since your decision procedure would still ‘force’ the predictor to predict you Left-box.
by running a simulation of you and seeing what that simulation did.
A simulation of your choice “upon seeing a bomb in the Left box under this scenario”? In that case, the choice to always take the Right box “upon seeing a bomb in the Left box under this scenario” is correct, and what any of the decision theories would recommend. Being in such a situation does necessitate the failure of the predictor, which means you are in a very improbable world, but that is not relevant to your decision in the world you happen to be in (simulated or not).
Or: A simulation of your choice in some different scenario (e.g. not seeing the contents of the boxes)? In that simulation, you would choose some box, but regardless of what that decision would happen to be, you are free to pick the Right box in this scenario, because it is a different scenario. Perhaps you picked Left in the alternative scenario, perhaps the predictor failed; neither is relevant here.
Why would any decision theory ever choose “Left” in this scenario?
Good point. It seems to me Left-boxing is still the right answer though, since your decision procedure would still ‘force’ the predictor to predict you Left-box.
What does it mean to Left-box, exactly? As in, under what specific scenarios are you making a choice between boxes, and choosing the Left box?