Hi Andrew,
I think that's a very accurate description of one of the problems in the RR prior computation. My only reservation is that I think it is too charitable to the Rank-Raglan argument which I consider the pineta of poor statistical reasoning
.
To use your notation, then what Carrier computes is that (I included b, background information):
P(A|b) = (1 + #historical RR heros) / (2+#RR heros)
Carrier notice that there are no historical RR heros and so concludes that P(A|b) = 1/(2+14) = 1/16.
The first point is that I think the conclusion should be read as follows: "Given that we only know about a character that he or she matches more than half of the RR criteria then there is about a 1/16 chance of the character being historical". I think that's a perfectly sensible statement.
The problem is that when we go from that statement to saying
p("Jesus existed" | b) = 1/16
we risk a huge bait-and-switch argument. How I think many would characterize this conclusion is: "The probability Jesus existed given our general background information is 1/16". However "our background knowledge" (more than 170 pages in OHJ) includes a ton of information about early Christians. As I read it, it for instance includes general information about the timing of the documents and general ideas about what early Christians believed. A point you brought up on your thread about the RR criteria is that if we evaluate the RR criteria using only Mark (and let's assume Mark was written first) it is much less obvious Jesus fits the RR hero class than if we use Matthew. I had not thought about that before, but it seems to be very important. However in the computation above it is just getting abstracted away along with every other piece of information (except the 22 RR factoids).
The second point is that I think there are good reasons to think that we aren't simply talking about a factor of 10. To connect your definitions to Carriers, Carriers theory of myth, ~h, is much more specific than simply C. If we apply the RR reference class computation to ~h we obtain:
P(~h|b) = (1 + #non-historical RR heros who matches the myth theory ~h) / (2+#RR heros)
However I can't see how any of the characters Carrier considers matches ~h and so we obtain:
P(~h|b) = (1 + 0) / (2+14) = 1/16
(which is roughly what you also used in your illustration). This result is different from what Carrier has, but nevertheless a great boost to Carriers myth theory: It shows the theory of myth is as plausible as the theory of historicity a-priori.
The elephant in the room is that the result reflects the 1+ in the numerator. I don't want to get too technical, but this number is really just reflecting other prior assumption and it is easy to think of situations where this type of reasoning goes very wrong.
I have a soft spot for conspiracies so as an example, suppose I wanted to compute the a-priori probability that the 9/11 attacks was carried out by terrorists vs. that they were an elaborate conspiracy carried out by the US government. As a reference class I use "Major attacks on large sky-scrapers in the past 100 years" (i.e. this is now 'b') and let's suppose there are 18 of these. Then I compare:
p("Terrorist attacks using several hijacked aircrafts" | b) = (1+0)/(2+18) = 1/20
and
p("Government conspiracy using several hijacked aircrafts" | b) = (1+0)/(2+18) = 1/20
and presto, using a bit of invalid statistical reasoning I just proved that my "us government conspiracy" is a-priori as likely as the official story. I can then go on to show that I can "explain" any evidence one can come up with ("the gubermint didit justlikethat!") and point out "difficulties" with the official story ("the buildings collapsed in free-fall speed! no large buildings have collapsed like that because of a fire!") and soon I will have proven the conspiracy true which I can announce as being based on "Bayesian probability theory and deductive logic" and so on. What I encountered here is the "reference class problem" and if one reads OHJ or PH it would seem not to be that noteworthy, however I think this and other examples shows that it is worth taking very serious.
This of course does not show the factor of 10 might not be correct in this case but here is a way to approach it: Suppose we decide to treat the RR characteristics (which as far as I know are found in the Gospels) as evidence and not as a means to compute the prior. Carrier claims we can do that and the result should come out the same. As a reference class I decide to use "Is a character found in literature". Then I decide the compute the prior of Carriers myth-theory ~h using this class:
P(~h|b="is a character found in literature")
The class of literary characters includes Zeus, Moses, Socrates, Robin hood, Goofy, Winston Churchill, Mickey-Mouse, etc. etc. Then we can ask how many of these matches ~h. ~h includes both that believers in the characters believe or teach a death and a burial in a supernatural realm (This would include some ancient Gods and with a bit of imagination also Aslan the Lion), but ~h also includes that subsequent communities came to believe the characters had had an earthly existence with companions, saying, etc (presumably we lost Aslan the lion and most other characters). Your guess is as good as mine, but I think the total number of literary characters outweighs those that matches ~h with orders of magnitude...
I think Zbykow (on the Vridar thread) is a good example of the types of objections Carrier would make to this example. Firstly, Zbykow/Carrier would point out that I focus on all of ~h and not just a particular feature of ~h (does not exist). I think this argument must rest upon a very peculiar idea about how probabilities are estimated from reference classes and it is extremely difficult to come up with any sort of general rule that would allow this type of inference and not be subject to very obvious paradoxes and fallacies. The "Bald man who likes RnB" example I have used on this thread is supposed to illustrate this.
Secondly, that "I did not account for information elsewhere correctly". I have asked Zbykow for about 20 posts exactly how we are supposed to account for the information elsewhere. His latest response: "Please, try to understand the basics first, then see if you still feel the need to rewrite any expressions.". I hope Carrier will eventually make us smarter on this point.
Thirdly, that "is a literary character" is not the proper reference class to use because the Rank-Raglan reference class is somehow intrinsically better because it is specific but not overly so... I think this argument is adequately met with: Says who?
The fundamental problem is that reference classes are not suitable to evaluate the probability of a complicated and specific hypothesis such as ~h or h based on specific information such as b (i.e. the reference class problem has, unsurprisingly, not vanished).
Cheers,
T.
