I think TDT also gets the wrong answer in the Parfit’s Hitchhiker case. Since it updates on the fact that the driver already brought it to the town, it believes that the logical fact of “I pay up” does not “go back in time” and affect the driver’s action. So the only relevant effect of paying up is losing money.
Unfortunately I could not find any definition of TDT online that is formal enough to determine how it acts in Parfit’s Hitchhiker or Counterfactual Mugging. In any case I don’t see how you can solve Parfit’s Hitchhiker without also solving Counterfactual Mugging. If you update on your observations and then look at the consequences of the logical node representing your decision, then you get both problems wrong; if you don’t update on your observations and just look at the consequences of the logical node representing your decision, then you get both problems right.
I’ve been thinking about this more. I think the distinction is that in Parfit’s Hitchhiker, if you try not to pay, you never find yourself in the situation of being able to not pay, but in Counterfactual Mugging, you can actually successfully not pay. But I think TDT constructs counterfactuals by considering different agents from the start of time, instead of considering different actions at the point of the decision. The kind of agent that one-boxes gets the million in Newcomb’s and the kind of agent that pays in Parfit’s ends up in town, but the kind of agent who pays in Counterfactual Mugging ends up $100 poorer. And only counterfactual agents are considered, not counterfactual coin flips.
TDT might or might not be well-defined in the case where the driver literally always predicts correctly, but if the driver is incorrect with probability 10−100 , then you don’t find yourself in the situation of not being able to pay by not paying up, if you are conditioning on your observations (the same way you have to in counterfactual mugging in order to not pay up). It reduces the a priori probability of your observations but this doesn’t matter if you update on them. There might be a decision theory other than UDT that takes this into account but I don’t know of it.
The kind of agent who pays in Counterfactual Mugging ends up $1000000 richer half the time, and $100 poorer half the time. Unless you are updating on which branch you are in, which means you should also update on the driver having picked you up.
Oh, I messed up. It’s Counterfactual Mugging that TDT doesn’t solve. I’ll edit the post.
I think TDT also gets the wrong answer in the Parfit’s Hitchhiker case. Since it updates on the fact that the driver already brought it to the town, it believes that the logical fact of “I pay up” does not “go back in time” and affect the driver’s action. So the only relevant effect of paying up is losing money.
Elizier seems to believe that his theory solves it, though I’m still unsure https://www.lesswrong.com/posts/c3wWnvgzdbRhNnNbQ/timeless-decision-theory-problems-i-can-t-solve
Unfortunately I could not find any definition of TDT online that is formal enough to determine how it acts in Parfit’s Hitchhiker or Counterfactual Mugging. In any case I don’t see how you can solve Parfit’s Hitchhiker without also solving Counterfactual Mugging. If you update on your observations and then look at the consequences of the logical node representing your decision, then you get both problems wrong; if you don’t update on your observations and just look at the consequences of the logical node representing your decision, then you get both problems right.
I’ve been thinking about this more. I think the distinction is that in Parfit’s Hitchhiker, if you try not to pay, you never find yourself in the situation of being able to not pay, but in Counterfactual Mugging, you can actually successfully not pay. But I think TDT constructs counterfactuals by considering different agents from the start of time, instead of considering different actions at the point of the decision. The kind of agent that one-boxes gets the million in Newcomb’s and the kind of agent that pays in Parfit’s ends up in town, but the kind of agent who pays in Counterfactual Mugging ends up $100 poorer. And only counterfactual agents are considered, not counterfactual coin flips.
TDT might or might not be well-defined in the case where the driver literally always predicts correctly, but if the driver is incorrect with probability 10−100 , then you don’t find yourself in the situation of not being able to pay by not paying up, if you are conditioning on your observations (the same way you have to in counterfactual mugging in order to not pay up). It reduces the a priori probability of your observations but this doesn’t matter if you update on them. There might be a decision theory other than UDT that takes this into account but I don’t know of it.
The kind of agent who pays in Counterfactual Mugging ends up $1000000 richer half the time, and $100 poorer half the time. Unless you are updating on which branch you are in, which means you should also update on the driver having picked you up.
You’re right, Parfit’s Hitchhiker with non-perfect predictive power is equivalent to Counterfactual Mugging.