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CuSithBell comments on Absence of Evidence Is Evidence of Absence - Less Wrong
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I don't like the way you describe that. It is confusing. The evidence is subversive activity. You cannot go out and look for no subversive activity, that makes no sense. You have to look for subversive activity. I'm not sure why you're fighting so hard for this point, since not finding something suggests just as much as finding something does. The only reason I suggest a change is for clarity. I don't want to think about no subversive activity and not no subversive activity, I want to think about subversive activity or no subversive activity. There is no difference, the second is simply less confusing.
E is subversive activity, and Warren's position is p(Q|~E).
Absolutely. I said so two posts up. The question is not about Q and R, though, it's about Q and ~Q.
But the whole argument is about the priors. The reason Warren's position is nonsensical is not because he believes a lack of subversion suggests some fact, it's that he argues that a lack of subversion suggests a fact, and then behaves in a manner counter to his argument. I've been arguing the fact that Warren argues p(Q|~E), But the reason he is locking up the Japanese-Americans is because he expects p(E|Q). The only way p(E|Q) makes any sense is if p(Q|E) is also true.
Warren's fundamental fear is based on p(E|Q) - that is, the 5th Column is plotting and scheming, and this will lead to subversion. The argument he uses to support this, however, is that p(Q|~E). The two positions are inversely related. If p(E|Q) is strong, then p(Q|~E) must be weak.
In other words, if p(E|Q) is strong, and p(Q) is high, then p(E) should be very high (because Q implies E), and p(~E) should be very small. Yet a very high ~E is used as evidence of p(Q). That makes no sense. If p(E|Q) is high, then ~E can exist in spite of Q, but it cannot exist because of Q.
The only way this is at all tenable is if p(E|Q) and p(~E|Q) are both true. In which case, neither E nor ~E is evidence of Q.
That's the whole point.
The whole point of this discussion is that his reasoning does not coincide with his actions. Thus one or the other is wrong.
Doesn't his position make sense if he believes that:
if there's no organized fifth column, we should see some intermittent, disorganized sabotage, and
if there is an organized fifth column, we should see NO sabotage before some date, at which there is a devastating attack
?
Of course, I agree that it's likely he would have made a different argument if he had seen evidence of sabotage - but as presented it seems his position is at least potentially coherent.
But what is the date? Is it 2 months? 6 months? A year? 5 years? What if it never happens? If nothing happens in 200 years, does that mean we must be absolutely certain that a fifth column is planning an attack?
It's not evidence, it's a lack of evidence. That's the point, and that's the problem.
Warren states it is his most ominous evidence that they are planning something. What evidence? It's not there, it doesn't exist. His whole position is based on the idea that the lack of evidence indicates they are planning something, yet he has nothing to suggest that such a lack of evidence indicates anything. The only thing the fact that they haven't attacked yet is evidence for is that they haven't attacked yet. Nothing more, nothing less, unless you have a pattern of behavior to base that on. There was no such pattern for the fifth column.
That's a different discussion. As you said,
I was simply arguing that your characterization of his argument as inherently self-contradictory was incorrect. Yeah, his supposed priors are probably wrong, but that's a different issue.
Okay, say it's 6 months. Does that make his argument non-contradictory?
If I predict it's going to rain soon because of a long dry spell, when it rains that doesn't prove me wrong.
Of course not, you have a pattern of weather to base that on, in which dry spells were consistently followed by rain.
Where is the basis for a lack of subversion? Historically, a lack of subversion has meant no subversion was ever planned, on what basis is this different for the 5th Column?
Yes, because now your evidence is that, if there is a 5th column, major subversion occurs every 6 months. This is testable.
His classification of a lack of subversion as evidence that the 5th Column is planning a major strike flies in the face of history - he has a small handful of anomalies to rely on. That's all.
I'll point to Eliezer's example of mammograms in his "Intuitive Explanation of Bayes Theorem" to help describe what I mean, particularly since it's pretty easy to find a very in-depth beysian analysis of this particular problem by Eliezer himself. In the example, 1% of women get breast cancer. 80% of the time a mammogram will test positive if a woman has breast cancer, 20% of the time it will test negative. 10% of the time a mammogram will test positive for someone who doesn't have breast cancer. This works out to a 7.8% likelihood that a woman has cancer if she gets a positive result on a mammogram. Conversely, getting a negative result on a mammogram results in a 0.22% likelihood that a woman has cancer.
In the Warren scenario, the 5th Column planning an attack is like the 1% breast cancer rate, and finding evidence of subversion is the mammogram. Not finding any evidence of subversion is the exact same as getting a negative on a mammogram in the breast cancer scenario. It has happened, sure, but it is extremely rare and in the vast majority of cases no subversion means no planned subversion. The problem is you don't have a history of major subversion without evidence of subversion. Throughout history it has been the exact opposite, therefore a lack of subversion must have a very low probability for preceding a major subversive attack.
Warren's position is like saying he believes there is a high risk of breast cancer because the mammogram came up negative. The only reasonable response to that is WTF? Yes, it's possible that the fifth column is planning something, but you cannot assume that because the evidence says otherwise, that's not reasonable at all. You can come to the conclusion through other evidence, but not with that evidence.
What Warren managed to do is take evidence that did not support his fear and claim that it did. It doesn't make any sense, it is an unreasonable position to take.
Now, if Warren had said "There is a very low likelihood that the 5th Column is planning a surprise attack, but I am not willing to take that risk" then it's an entirely different situation, and that is a completely reasonable response. If breast cancer means being forced to fight through Dante's 9 levels of hell, then it might be worth a double-mastectomy in spite of the 1 in 500 chance that it would happen.
I was wrong when I said that a single case of subversion falsifies his position. Obviously surprise attacks exist, so that was clearly incorrect, and I think it led to a lot of the disagreement in the discussion. I was looking at the problem too narrowly. However the reason surprise attacks are a surprise is because they are very rare, so the fact that nothing has happened must still overwhelmingly support the idea that nothing will happen. In other words, it is overwhelming evidence against an attack, not for it. That's the only reason surprise attacks work at all, because you you have no evidence to suggest they are coming (and that they haven't attacked is not such evidence).
Hopefully I've explained myself adequately now.