You seem to have misunderstood the problem statement [1]. If you commit to doing “FDT, except that if the predictor makes a mistake and there’s a bomb in the Left, take Right instead”, then you will almost surely have to pay $100 (since the predictor predicts that you will take Right), whereas if you commit to using pure FDT, then you will almost surely have to pay nothing (with a small chance of death). There really is no “strategy that, if the agent commits to it before the predictor makes her prediction, does better than FDT”.
[1] Which is fair enough, as it wasn’t actually specified correctly: the predictor is actually trying to predict whether you will take Left or Right if it leaves its helpful note, not in the general case. But this assumption has to be added, since otherwise FDT says to take Right.
It sounds like you’re saying that I correctly understood the problem statement as it was written (but it was written incorrectly); but that the post erroneously claims that in the scenario as (incorrectly) written, FDT says to take Left, when in fact FDT in that scenario-as-written says to take right. Do I understand you?
But this assumption has to be added, since otherwise FDT says to take Right.
Why? FDT isn’t influenced in its decision by the note, so there is no loss of subjunctive dependence when this assumption isn’t added. (Or so it seems to me: I am operating at the limits of my FDT-knowledge here.)
FDT, except that if the predictor makes a mistake and there’s a bomb in the Left, take Right instead.
How would this work? Your strategy seems to be “Left-box unless the note says there’s a bomb in Left”. This ensures the predictor is right whether she puts a bomb in Left or not, and doesn’t optimize expected utility.
It costs you p * $100 for 0 ⇐ p ⇐ 1 where p depends on how “mean” you believe the predictor is.
Left-boxing costs 10^-24 * $1,000,000 = $10^-18 if you value life at a million dollars. Then if p > 10^-20, Left-boxing beats your strategy.
Note that FDT Right-boxes when you give life infinite value.
What’s special in this scenario with regards to valuing life finitely?
If you always value life infinitely, it seems to me all actions you can ever take get infinite values, as there is always a chance you die, which makes decision making on basis of utility pointless.
FDT, except that if the predictor makes a mistake and there’s a bomb in the Left, take Right instead.
Unfortunately, that doesn’t work. The predictor, if malevolent, could then easily make you choose right and pay a $100.
Left-boxing is the best strategy possible as far as I can tell. As in, yes, that extremely unlikely scenario where you burn to death sucks big time, but there is no better strategy possible (unless there is a superior strategy I—and it appears everybody—haven’t/hasn’t thought of).
If you commit to taking Left, then the predictor, if malevolent, can “mistakenly” “predict” that you’ll take Right, making you burn to death. Just like in the given scenario: “Whoops, a mistaken prediction! How unfortunate and improbable! Guess you have no choice but to kill yourself now, how sad…”
There absolutely is a better strategy: don’t knowingly choose to burn to death.
For the record, I read Nate’s comments again, and I now think of it like this:
To the extent that the predictor was accurate in her line of reasoning, then you left-boxing does NOT result in you slowly burning to death. It results in, well, the problem statement being wrong, because the following can’t all be true:
The predictor is accurate
The predictor predicts you right-box, and places the bomb in left
You left-box
And yes, apparently the predictor can be wrong, but I’d say, who even cares? The probability of the predictor being wrong is supposed to be virtually zero anyway (although as Nate notes, the problem description isn’t complete in that regard).
It’s preventable by taking the Right box. If you take Left, you burn to death. If you take Right, you don’t burn to death.
Totally, here it is:
FDT, except that if the predictor makes a mistake and there’s a bomb in the Left, take Right instead.
You seem to have misunderstood the problem statement [1]. If you commit to doing “FDT, except that if the predictor makes a mistake and there’s a bomb in the Left, take Right instead”, then you will almost surely have to pay $100 (since the predictor predicts that you will take Right), whereas if you commit to using pure FDT, then you will almost surely have to pay nothing (with a small chance of death). There really is no “strategy that, if the agent commits to it before the predictor makes her prediction, does better than FDT”.
[1] Which is fair enough, as it wasn’t actually specified correctly: the predictor is actually trying to predict whether you will take Left or Right if it leaves its helpful note, not in the general case. But this assumption has to be added, since otherwise FDT says to take Right.
It sounds like you’re saying that I correctly understood the problem statement as it was written (but it was written incorrectly); but that the post erroneously claims that in the scenario as (incorrectly) written, FDT says to take Left, when in fact FDT in that scenario-as-written says to take right. Do I understand you?
Yes.
Why? FDT isn’t influenced in its decision by the note, so there is no loss of subjunctive dependence when this assumption isn’t added. (Or so it seems to me: I am operating at the limits of my FDT-knowledge here.)
How would this work? Your strategy seems to be “Left-box unless the note says there’s a bomb in Left”. This ensures the predictor is right whether she puts a bomb in Left or not, and doesn’t optimize expected utility.
It doesn’t kill you in a case when you can choose not to be killed, though, and that’s the important thing.
It costs you p * $100 for 0 ⇐ p ⇐ 1 where p depends on how “mean” you believe the predictor is. Left-boxing costs 10^-24 * $1,000,000 = $10^-18 if you value life at a million dollars. Then if p > 10^-20, Left-boxing beats your strategy.
Why would I value my life finitely in this case? (Well, ever, really, but especially in this scenario…)
Also, were you operating under the life-has-infinite-value assumption all along? If so, then
You were incorrect about FDT’s decision in this specific problem
You should probably have mentioned you had this unusual assumption, so we could have resolved this discussion way earlier
Note that FDT Right-boxes when you give life infinite value.
What’s special in this scenario with regards to valuing life finitely?
If you always value life infinitely, it seems to me all actions you can ever take get infinite values, as there is always a chance you die, which makes decision making on basis of utility pointless.
Unfortunately, that doesn’t work. The predictor, if malevolent, could then easily make you choose right and pay a $100.
Left-boxing is the best strategy possible as far as I can tell. As in, yes, that extremely unlikely scenario where you burn to death sucks big time, but there is no better strategy possible (unless there is a superior strategy I—and it appears everybody—haven’t/hasn’t thought of).
If you commit to taking Left, then the predictor, if malevolent, can “mistakenly” “predict” that you’ll take Right, making you burn to death. Just like in the given scenario: “Whoops, a mistaken prediction! How unfortunate and improbable! Guess you have no choice but to kill yourself now, how sad…”
There absolutely is a better strategy: don’t knowingly choose to burn to death.
We know the error rate of the predictor, so this point is moot.
I still have to see a strategy incorporating this that doesn’t overall lose by losing utility in other scenarios.
How do we know it? If the predictor is malevolent, then it can “err” as much as it wants.
For the record, I read Nate’s comments again, and I now think of it like this:
To the extent that the predictor was accurate in her line of reasoning, then you left-boxing does NOT result in you slowly burning to death. It results in, well, the problem statement being wrong, because the following can’t all be true:
The predictor is accurate
The predictor predicts you right-box, and places the bomb in left
You left-box
And yes, apparently the predictor can be wrong, but I’d say, who even cares? The probability of the predictor being wrong is supposed to be virtually zero anyway (although as Nate notes, the problem description isn’t complete in that regard).
We know it because it is given in the problem description, which you violate if the predictor ‘can “err” as much as it wants’.