The latter seems to be the most intuitively correct rule
So if I extract an red ball from an urn, should I condition the probability of finding a black ball in the next turn on not having extracted a red ball?
Besides, P(H) is most definitely not equal to P(H|E). P(H) is on the other hand demonstrably equal to P(H|E)P(E)+P(H|-E)P(-E), the usual decomposition of unity. I think we are talking about two completely different things here.
I’m talking about the following issue, found at this link:
A. The problem of uncertain evidence. The Simple Principle of Conditionalization requires that the acquisition of evidence be representable as changing one’s degree of belief in a statement E to one — that is, to certainty. But many philosophers would object to assigning probability of one to any contingent statement, even an evidential statement, because, for example, it is well-known that scientists sometimes give up previously accepted evidence. Jeffrey has proposed a generalization of the Principle of Conditionalization that yields that principle as a special case. Jeffrey’s idea is that what is crucial about observation is not that it yields certainty, but that it generates a non-inferential change in the probability of an evidential statement E and its negation ~E (assumed to be the locus of all the non-inferential changes in probability) from initial probabilities between zero and one to Pf(E) and Pf(~E) = [1 − Pf(E)]. Then on Jeffrey’s account, after the observation, the rational degree of belief to place in an hypothesis H would be given by the following principle:
Principle of Jeffrey Conditionalization:
Pf(H) = Pi(H/E) × Pf(E) + Pi(H/~E) × Pf(~E) [where E and H are both assumed to have prior probabilities between zero and one]
Counting in favor of Jeffrey’s Principle is its theoretical elegance. Counting against it is the practical problem that it requires that one be able to completely specify the direct non-inferential effects of an observation, something it is doubtful that anyone has ever done. Skyrms has given it a Dutch Book defense.
So if I extract an red ball from an urn, should I condition the probability of finding a black ball in the next turn on not having extracted a red ball?
Besides, P(H) is most definitely not equal to P(H|E). P(H) is on the other hand demonstrably equal to P(H|E)P(E)+P(H|-E)P(-E), the usual decomposition of unity. I think we are talking about two completely different things here.
I’m talking about the following issue, found at this link: