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nyan_sandwich comments on Many Weak Arguments vs. One Relatively Strong Argument - Less Wrong
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Suppose:
P(penrose says | consciousness & expertise is general) = 0.5
P(penrose says | ~consiousness & expertise is general) = 0
ie. if expertise is general, penrose's opinion is infinitely strong evidence.
P(penrose says | consc & expertise is narrow) = 0.5
P(penrose says | ~ consc & expertise is narrow) = 0.25
ie. if expertise is narrow, penrose's opinion is weak evidence.
Then suppose 90% chance that expertise is general. ie. We are somehow quite sure that experts are never wrong. (quite sure that the argument that expertise is narrow is wrong)
Then:
P(penrose says | consc) = 0.5
P(penrose says | ~consc) = ~0.025
ie. even under these extremely charitable assumptions, Penrose's opinion is only 20x (medium) evidence.
Your assumptions are much more reasonable than I have used here, and will give you correspondingly weaker evidence.
And then, why privilege penrose over the ~1e3 experts who disagree with him?
EDIT: If I were charitable, then I'd note that this argument applies to all arguments, including those on the other side; that strong evidence is in general quite hard to find unless you are very sure of your experimental apparatus.
It is valuable to have a list of "people who believe X" and "people who believe ~X," and one might suspect that, if X, the majority position, is incorrect, the people on the ~X list to disproportionately be higher quality. I'm not a good enough science historian to know if that's the case historically, especially because you would want to use contemporary measurements of quality, as many people who believed ~X and it turned out to be right are more highly estimated by hindsight.
(More broadly, there may be systematic patterns to public support on scientific controversies, such that 1) one shouldn't compare length of lists or treat positions of individuals as giving completely independent evidence and 2) there may be patterns that suggest known kinds of events.)