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thomblake comments on Absence of Evidence Is Evidence of Absence - Less Wrong
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This article makes a very good point very well. If E would be evidence for a hypothesis H, then ~E has to be evidence for ~H.
Unfortunately, I think that it is unfair to read Warren as violating this principle. (I say "Unfortunately" because it would be nice to have such an evocative real example of this fallacy.)
I think that Warren's reasoning is more like the following: Based on theoretical considerations, there is a very high probability P(H) that there is a fifth column. The theoretical considerations have to do with the nature of the Japanese–American conflict and the opportunities available to the Japanese. Basically, there mere fact that the Japanese have both means and motive is enough to push P(H) up to a high value.
Sure, the lack of observed sabotage (~E) makes P(H|~E) < P(H). So the probability of a fifth column goes down a bit. But P(H) started out so high that H is still the only contingency that we should really worry about. The only important question left is, Given that there is a fifth column, is it competent or incompetent? Does the observation of ~E mean that we are in more danger or less danger? That is, letting C = "The fifth column is competent", do we have that P(C | ~E & H) > P(C | H)?
Warren is arguing that ~E should lead us to anticipate a more dangerous fifth column. He is saying that an incompetent fifth column would probably have performed minor sabotage, which would have left evidence. A competent fifth column, on the other hand, would probably still be marshaling its forces to strike a major blow, which would be inconsistent with E. Hence, P(C | ~E & H) > P(C | H). That is why ~E is a greater cause for concern than E would have been.
Whether all of these prior probabilities are reasonable is another matter. But Warren's remarks are consistent with correct Bayesian reasoning from those priors.
While I think your reading is consistent with a very generous application of the principle of charity, I'm not certain it's appropriate in this case to so apply. Do you have any evidence that Warren was reasoning in this way rather than the less-charitable version, and if so, why didn't he say so explicitly?
It really seems like the simpler explanation is fear plus poor thinking.
Sorry for taking so long to reply to this.
I think that a close and strict reading supports my interpretation. I don't see the need for an unduly charitable reading.
First, I assume the following context for the quote: Warren had argued for (or maybe only claimed) a high probability for the proposition that there is a Japanese fifth column within the US. Let R be this italicized proposition. Then Warren has argued that p(R) >> 0.
Given that context, here is how I parse the quote, line-by-line:
I take the questioner to be asserting that there has been no observed sabotage or any other type of espionage by Japanese-Americans up to that time. Let E be this proposition.
Warren responds:
I take Warren to be saying that the expected cost of not interring Japanese-Americans is significantly higher after we update on E than it was before we updated on E. Letting D be the "default" action in which we don't inter Japanese-Americans, Warren is asserting that EU(D | E) << EU(D).
The above assertion is the conclusion of Warren's reasoning. If we can show that this conclusion follows from correct Bayesian reasoning from a psychologically realistic prior, plus whatever evidence he explicitly adduces, then the quote cannot serve as an example of the fallacy that Eliezer describes in this post.
Now, we may think that that "psychologically realistic prior" is very probably based in turn on "fear plus poor thinking". But Warren doesn't explicitly show us where his prior came from, so the quote in and of itself is not an example of an explicit error in Bayesian reasoning. Whatever fallacious reasoning occurred, it happened "behind the scenes", prior to the reasoning on display in the quote.
Continuing with my parsing, Warren goes on to say:
Let Q be the proposition that there is a Japanese fifth column in America, and it will perform a timed attack, but right now it is lulling us into a false sense of security.
I take Warren to be claiming that p(Q | E) >> p(Q), and that p(Q | E) is sufficiently large to justify saying "I believe Q".
It remains only to give a psychologically realistic prior distribution p such the claims above follow — that is, we need that
This will suffice to invalidate the Warren quote as an example for this post.
It is a mathematical fact that such priors exist in an abstract sense. Do you think it unlikely that such a prior is psychologically realistic for someone in Warren's position? I think that selection effects and standard human biases make it very plausible that someone in his position would have such a prior.
If you're still skeptical, we can discuss which priors are psychologically realistic for someone in Warren's position.