The main edit I would make to EY’s point is that we are really considering 3 hypotheses here, not just two. H1 is that a Japanese fifth column exists and is currently actively engaged in covert operations. H2 is that no fifth column exists. H3 is that a fifth column exists and is remaining low profile and organizing in preparation for covert operations. In this analysis, P(H3) < P(any fifth column exists), because it specifies an additional detail. However P(E|H3) is about equal to P(E|H2) (a secretive fifth column might generate some minor acts of sabotage, but so could a few disorganized malcontents). In that case, the observation ~E would pull probability mass away from H1 and towards H2 and H3, but H2 and H3 would not gain or lose probability mass relative to each other. In this case, the debate would then center on the question of our prior probabilities for H2 relative to H3, and P(H3|I) is almost certainly less than P(H2|I).
The main edit I would make to EY’s point is that we are really considering 3 hypotheses here, not just two. H1 is that a Japanese fifth column exists and is currently actively engaged in covert operations. H2 is that no fifth column exists. H3 is that a fifth column exists and is remaining low profile and organizing in preparation for covert operations. In this analysis, P(H3) < P(any fifth column exists), because it specifies an additional detail. However P(E|H3) is about equal to P(E|H2) (a secretive fifth column might generate some minor acts of sabotage, but so could a few disorganized malcontents). In that case, the observation ~E would pull probability mass away from H1 and towards H2 and H3, but H2 and H3 would not gain or lose probability mass relative to each other. In this case, the debate would then center on the question of our prior probabilities for H2 relative to H3, and P(H3|I) is almost certainly less than P(H2|I).
I agree. We discussed this point in this thread of the original post:
http://lesswrong.com/lw/ih/absence_of_evidence_is_evidence_of_absence/35ra