If I understand correctly, Carrier believes that using a reference class of "Josephus-mentioners" (or something else) and putting the Rank-Raglan data in the consideration of conditional probabilities, or doing the reverse and putting the "Rank-Raglan reference class" as the benchmark for prior probability and using the "Josephus-mentioning" data in the consideration of posterior probabilities... would be roughly/exactly (I think he assumes exactly) equivalent when it comes to the resulting posterior probability calculation.
That's also how I understand Carrier. I don't want to hedge everything I write, but the argument depends on how we compute probabilities from reference classes so I will return to that later.
The part of the argument I think is uncontroversial is that if we re-write the probabilities with the product rule so we for instance have a term like: p(h|"Josepheus-information") or p(h|"Rank-Raglan-information") then the result is guaranteed to be consistent
as statements about unknown probabilities
This changes when we estimate the probabilities from for instance reference classes or guess them or what we choose to do. The way I understand a reference class to work I don't think this in itself is such a big deal (in itself) if we use sensible reference classes.
This brings me to the issue of how reference classes work to approximate probabilities. If I was going to use reference classes I would go with the simplest solution and just say:
P(A|B) = (elements that matches A and B) / (Elements that matches B)
Where I disagree with OHJ is that I think it deviates from the above in two important ways. First, that when we re-write probabilities (like use the Josepheus prior or the Rank-Raglan prior) we have to do it with the product rule and keep track of the various terms.. as I see it the terms we arrive at are complicated (not formally of course, but in terms of actually assigning numerical values) and this issues should at least be acknowledged.
The second issue is that I think Carrier deviates from the simple way of computing probabilities from reference classes. Carriers estimate of the conditional probability is:
p(~h|b) = (1 + RR heroes that exist) / ( 2 + RR heroes).
I think this deviation is significant because ~h is Carriers hypothesis of myth which is defined to include specific pieces of information such as "incarnated, died, buried and resurrected in the supernatural realm". Put bluntly, when Carrier says that 15 Rank-Raglan heroes counts towards ~h, to my mind that must imply they match ~h and therefore that for instance Moses (who are amongst the Rank-Raglan heroes) died in the supernatural realm. Then there is also the issue of how b is contracted to be only the information that places Jesus in the Rank-Raglan hero class. This is not the end of the story.. the discussion is partly complicated because Carrier do not explicitly state how we compute a conditional probability from a reference class in general and so some guesswork is involved.
