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?
Okay, say it's 6 months. Does that make his argument non-contradictory?
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.
From Robyn Dawes’s Rational Choice in an Uncertain World:
Consider Warren’s argument from a Bayesian perspective. When we see evidence, hypotheses that assigned a higher likelihood to that evidence gain probability, at the expense of hypotheses that assigned a lower likelihood to the evidence. This is a phenomenon of relative likelihoods and relative probabilities. You can assign a high likelihood to the evidence and still lose probability mass to some other hypothesis, if that other hypothesis assigns a likelihood that is even higher.
Warren seems to be arguing that, given that we see no sabotage, this confirms that a Fifth Column exists. You could argue that a Fifth Column might delay its sabotage. But the likelihood is still higher that the absence of a Fifth Column would perform an absence of sabotage.
Let E stand for the observation of sabotage, and ¬E for the observation of no sabotage. The symbol H1 stands for the hypothesis of a Japanese-American Fifth Column, and H2 for the hypothesis that no Fifth Column exists. The conditional probability P(E | H), or “E given H,” is how confidently we’d expect to see the evidence E if we assumed the hypothesis H were true.
Whatever the likelihood that a Fifth Column would do no sabotage, the probability P(¬E | H1), it won’t be as large as the likelihood that there’s no sabotage given that there’s no Fifth Column, the probability P(¬E | H2). So observing a lack of sabotage increases the probability that no Fifth Column exists.
A lack of sabotage doesn’t prove that no Fifth Column exists. Absence of proof is not proof of absence. In logic, (A ⇒ B), read “A implies B,” is not equivalent to (¬A ⇒ ¬B), read “not-A implies not-B .”
But in probability theory, absence of evidence is always evidence of absence. If E is a binary event and P(H | E) > P(H), i.e., seeing E increases the probability of H, then P(H | ¬ E) < P(H), i.e., failure to observe E decreases the probability of H . The probability P(H) is a weighted mix of P(H | E) and P(H | ¬ E), and necessarily lies between the two.1
Under the vast majority of real-life circumstances, a cause may not reliably produce signs of itself, but the absence of the cause is even less likely to produce the signs. The absence of an observation may be strong evidence of absence or very weak evidence of absence, depending on how likely the cause is to produce the observation. The absence of an observation that is only weakly permitted (even if the alternative hypothesis does not allow it at all) is very weak evidence of absence (though it is evidence nonetheless). This is the fallacy of “gaps in the fossil record”—fossils form only rarely; it is futile to trumpet the absence of a weakly permitted observation when many strong positive observations have already been recorded. But if there are no positive observations at all, it is time to worry; hence the Fermi Paradox.
Your strength as a rationalist is your ability to be more confused by fiction than by reality; if you are equally good at explaining any outcome you have zero knowledge. The strength of a model is not what it can explain, but what it can’t, for only prohibitions constrain anticipation. If you don’t notice when your model makes the evidence unlikely, you might as well have no model, and also you might as well have no evidence; no brain and no eyes.
1 If any of this sounds at all confusing, see my discussion of Bayesian updating toward the end of The Machine in the Ghost, the third volume of Rationality: From AI to Zombies.