Here’s a modified version. Instead of a smoking lesion, there’s a “jump into active volcano lesion”. Furthermore, the correlation isn’t as puny as for the smoking lesion. 100% of people with this lesion jump into active volcanoes and die, and nobody else does.
Should you go jump into an active volcano?
Using a decision theory to figure out what decision you should make assumes that you’re capable of making a decision. “The lesion causes you to jump into an active volcano/smoke” and “you can choose whether to jump into an active volcano/smoke” are contradictory. Even “the lesion is correlated (at less than 100%) with jumping into an active volcano/smoking” and “you can choose whether to jump into an active volcano/smoke” are contradictory unless “is correlated with” involves some correlation for people who don’t use decision theory and no correlation for people who do.
Using a decision theory to figure out what decision you should make assumes that you’re capable of making a decision.
Agreed.
unless “is correlated with” involves some correlation for people who don’t use decision theory and no correlation for people who do.
Doesn’t this seem sort of realistic, actually? Decisions made with System 1 and System 2, to use Kahneman’s language, might have entirely different underlying algorithms. (There is some philosophical trouble about how far we can push the idea of an ‘intervention’, but I think for human-scale decisions there is a meaningful difference between interventions and observations such that CDT distinguishing between them is a feature.)
This maps onto an objection by proponents of EDT that the observational data might not be from people using EDT, and thus the correlation may disappear when EDT comes onto the stage. I think that objection proves too much- suppose all of our observational data on the health effects of jumping off cliffs comes from subjects who were not using EDT (suppose they were drunk). I don’t see a reason inside the decision theory for differentiating between the effects of EDT on the correlation between jumping off the cliff and the effects of EDT on the correlation between smoking and having the lesion.
These two situations correspond to two different causal structures—Drunk → Fall → Death and Smoke ← Lesion → Cancer—which could have the same joint probability distribution. The directionality of the arrow is something that CDT can make use of to tell that the two situations will respond differently to interventions at Drunk and Smoke: it is dangerous to be drunk around cliffs, but not to smoke (in this hypothetical world).
EDT cannot make use of those arrows. It just has Drunk—Fall—Death and Smoke—Lesion—Cancer (where it knows that the correlations between Drunk and Death are mediated by Fall, and the correlations between Smoke and Cancer are mediated by Lesion). If we suppose that adding an EDT node might mean that the correlation between Smoke and Lesion (and thus Cancer) might be mediated by EDT, then we must also suppose that adding an EDT node might mean that the correlation between Drunk and Fall (and thus Death) might be mediated by EDT.
(I should point out that the EDT node describes whether or not EDT was used to decide to drink, not to decide whether or not to fall off the cliff, by analogy of using EDT to decide whether or not to smoke, rather than deciding whether or not to have a lesion.)
Here’s a modified version. Instead of a smoking lesion, there’s a “jump into active volcano lesion”. Furthermore, the correlation isn’t as puny as for the smoking lesion. 100% of people with this lesion jump into active volcanoes and die, and nobody else does.
Should you go jump into an active volcano?
Using a decision theory to figure out what decision you should make assumes that you’re capable of making a decision. “The lesion causes you to jump into an active volcano/smoke” and “you can choose whether to jump into an active volcano/smoke” are contradictory. Even “the lesion is correlated (at less than 100%) with jumping into an active volcano/smoking” and “you can choose whether to jump into an active volcano/smoke” are contradictory unless “is correlated with” involves some correlation for people who don’t use decision theory and no correlation for people who do.
Agreed.
Doesn’t this seem sort of realistic, actually? Decisions made with System 1 and System 2, to use Kahneman’s language, might have entirely different underlying algorithms. (There is some philosophical trouble about how far we can push the idea of an ‘intervention’, but I think for human-scale decisions there is a meaningful difference between interventions and observations such that CDT distinguishing between them is a feature.)
This maps onto an objection by proponents of EDT that the observational data might not be from people using EDT, and thus the correlation may disappear when EDT comes onto the stage. I think that objection proves too much- suppose all of our observational data on the health effects of jumping off cliffs comes from subjects who were not using EDT (suppose they were drunk). I don’t see a reason inside the decision theory for differentiating between the effects of EDT on the correlation between jumping off the cliff and the effects of EDT on the correlation between smoking and having the lesion.
These two situations correspond to two different causal structures—Drunk → Fall → Death and Smoke ← Lesion → Cancer—which could have the same joint probability distribution. The directionality of the arrow is something that CDT can make use of to tell that the two situations will respond differently to interventions at Drunk and Smoke: it is dangerous to be drunk around cliffs, but not to smoke (in this hypothetical world).
EDT cannot make use of those arrows. It just has Drunk—Fall—Death and Smoke—Lesion—Cancer (where it knows that the correlations between Drunk and Death are mediated by Fall, and the correlations between Smoke and Cancer are mediated by Lesion). If we suppose that adding an EDT node might mean that the correlation between Smoke and Lesion (and thus Cancer) might be mediated by EDT, then we must also suppose that adding an EDT node might mean that the correlation between Drunk and Fall (and thus Death) might be mediated by EDT.
(I should point out that the EDT node describes whether or not EDT was used to decide to drink, not to decide whether or not to fall off the cliff, by analogy of using EDT to decide whether or not to smoke, rather than deciding whether or not to have a lesion.)