(Here’s a slightly less mind-killing variant: let’s say that regularly taking aspirin is correlated with risk of a heart attack, but not because it causes them; in fact, aspirin (in this hypothetical) is good for anyone’s heart. Instead, there’s an additional risk factor for heart attacks, which also causes discomfort beneath the threshold of full consciousness. People with this risk factor end up being more likely to take aspirin regularly, though they’re not able to pinpoint why, and the effect is large enough that the correlation points the “wrong” way. Now if you know all of this and are wondering whether to take aspirin regularly, the calculation you did above would tell you not to take it!)
We can get down to a discussion of evidential vs casual decision theory if you want, certainly, but I think that’s a bit off topic.
I have a couple of reactions to your point. My initial reaction is that evidential decision theory is superior in the case of Omega because nothing is known about em. Since Omega is a black box, the only thing that can really be done is gather evidence and respond to it.
But more generally, I think your example is somewhat strawman-ish. Just like in the smoking problem, there is other evidence suggesting that Asprin has the opposite effect. Saying that evidential decision theory has to ignore this is pretty unfair to it. Furthermore, you know that you can’t really rely on the evidence you have (that Asprin is correlated with heart attack, because you know you don’t have a random sample. Moreover, the evidence that Asprin is actually good for your heart was supposedly generated with some kind of statistical controls. It’s the same reason I mentioned in my analysis the assumption that Omega knows nothing more or less about you than ey did about any of the other people. The second you don’t have a representative sample, all of your statistics can be thrown out of the window.
This looks like evidential decision theory, which gives the wrong answer in the Smoking Lesion problem.
(Here’s a slightly less mind-killing variant: let’s say that regularly taking aspirin is correlated with risk of a heart attack, but not because it causes them; in fact, aspirin (in this hypothetical) is good for anyone’s heart. Instead, there’s an additional risk factor for heart attacks, which also causes discomfort beneath the threshold of full consciousness. People with this risk factor end up being more likely to take aspirin regularly, though they’re not able to pinpoint why, and the effect is large enough that the correlation points the “wrong” way. Now if you know all of this and are wondering whether to take aspirin regularly, the calculation you did above would tell you not to take it!)
We can get down to a discussion of evidential vs casual decision theory if you want, certainly, but I think that’s a bit off topic.
I have a couple of reactions to your point. My initial reaction is that evidential decision theory is superior in the case of Omega because nothing is known about em. Since Omega is a black box, the only thing that can really be done is gather evidence and respond to it.
But more generally, I think your example is somewhat strawman-ish. Just like in the smoking problem, there is other evidence suggesting that Asprin has the opposite effect. Saying that evidential decision theory has to ignore this is pretty unfair to it. Furthermore, you know that you can’t really rely on the evidence you have (that Asprin is correlated with heart attack, because you know you don’t have a random sample. Moreover, the evidence that Asprin is actually good for your heart was supposedly generated with some kind of statistical controls. It’s the same reason I mentioned in my analysis the assumption that Omega knows nothing more or less about you than ey did about any of the other people. The second you don’t have a representative sample, all of your statistics can be thrown out of the window.