Yes, “same evidence” in this context implies that it is usable in the same bayesean updates in the same way.
If two different bayeseans have the same priors and the same evidence, they will agree.
Please see this section about Professor Jaynes’ view of priors from Wikipedia: https://en.wikipedia.org/wiki/Prior_probability#Uninformative_priors
Essentially, he says that it is impossible for two people with the same information to have different priors and instead should use the same “objective prior”. Same idea for evidence as well
Yes, “same evidence” in this context implies that it is usable in the same bayesean updates in the same way.
Please see this section about Professor Jaynes’ view of priors from Wikipedia: https://en.wikipedia.org/wiki/Prior_probability#Uninformative_priors
Essentially, he says that it is impossible for two people with the same information to have different priors and instead should use the same “objective prior”. Same idea for evidence as well