Considering something impossible is necessary to decision theory.
Paraphrasing Drescher: Since I am rational, it is impossible that I will walk into the street while I can see traffic. I have failed to do so 100⁄100 times before. Therefore, it is impossible that I get hit by traffic, therefore I should cross the street. BLAM
It is, however, worth making a distinction between something impossible due to a known fact about the world not including from you, and something impossible because it results from an action you’ll never take. The latter leads to paradoxes like the above; since, obviously, if I do in fact walk into the street when I can see traffic, then it’s not in fact impossible for me to walk into the street when I can see traffic. This results from the agents conditioning on incorrect evidence (whose incorrectness results from the agent’s decision, which results in part from the evidence...); the way this is dealt with in Ambient Decision Theory is to ban considering the results of an agents actions as part of the world, and instead requiring that they be reconstructed each time they are called (see the second and third sections of this post).
While it’s technically possible for a similar process to occur in the world, it’s fairly clear that it’s not occurring here: while the initial state of the world does depend on the agent’s decision, the problem explicitly states that it’s impossible for such a paradox to result, as the decision Omega is conditioning on is always the same as the one that the agent eventually makes.
the way this is dealt with in Ambient Decision Theory is to ban considering the results of an agents actions as part of the world, and instead requiring that they be reconstructed each time they are called
I wouldn’t say it like that, since the actions must already be part of the world (its properties following from the definition), the agent just can’t figure out what they are, can’t resolve that particular logical uncertainty. See “Against counterfactuals”: everything should be already determined, as variations of the decision problem have nothing to do with the actual decision problem.
Considering something impossible is necessary to decision theory.
Paraphrasing Drescher: Since I am rational, it is impossible that I will walk into the street while I can see traffic. I have failed to do so 100⁄100 times before. Therefore, it is impossible that I get hit by traffic, therefore I should cross the street. BLAM
It is, however, worth making a distinction between something impossible due to a known fact about the world not including from you, and something impossible because it results from an action you’ll never take. The latter leads to paradoxes like the above; since, obviously, if I do in fact walk into the street when I can see traffic, then it’s not in fact impossible for me to walk into the street when I can see traffic. This results from the agents conditioning on incorrect evidence (whose incorrectness results from the agent’s decision, which results in part from the evidence...); the way this is dealt with in Ambient Decision Theory is to ban considering the results of an agents actions as part of the world, and instead requiring that they be reconstructed each time they are called (see the second and third sections of this post).
While it’s technically possible for a similar process to occur in the world, it’s fairly clear that it’s not occurring here: while the initial state of the world does depend on the agent’s decision, the problem explicitly states that it’s impossible for such a paradox to result, as the decision Omega is conditioning on is always the same as the one that the agent eventually makes.
I wouldn’t say it like that, since the actions must already be part of the world (its properties following from the definition), the agent just can’t figure out what they are, can’t resolve that particular logical uncertainty. See “Against counterfactuals”: everything should be already determined, as variations of the decision problem have nothing to do with the actual decision problem.