I agree that Jordan’s equation needs to be adjusted (corrected), but I humbly suggest that in this context, it is better to adjust it to the product rule:
Yes, correct. I missed that. For the standard Doomsday Argument P(B|O) is probably 1, so it can be excluded, but for alternative classes of people this isn’t so.
Maybe I’m misreading this, but it looks like you’re missing a term...
You said: P(O) = P(B) * P(O|B)
Bayes’s theorem: P(O) P(B|O) = P(B) P(O|B)
ne?
I agree that Jordan’s equation needs to be adjusted (corrected), but I humbly suggest that in this context, it is better to adjust it to the product rule:
P(O and B) = P(B) * P(O|B).
ADDED. Yeah, minor point.
Yes, correct. I missed that. For the standard Doomsday Argument P(B|O) is probably 1, so it can be excluded, but for alternative classes of people this isn’t so.