Before we begin, I emphasize that the answers you give to the questions I ask you about your uncertainty are yours alone, and need not be the same as what someone else would say, even someone with the same information as you have, and facing the same decisions.

- Principles of Uncertainty, page 1, emphasis added

I attended a statistics conference in January at which Jay Kadane (in attendence) was described as one of the last still-living original subjective Bayesians. I'm not sure how many currently practicing Bayesian hold to this line. For example, Brad Carlin, an organizer of said conference, mentioned Kadane's philosophical stance in this comment about a book he (Carlin) wrote:

... Don [Berry, who got his Ph.D. under Kadane] gave me some older "white papers" he'd written on this subject for introductory audiences, but never published. I took these and edited/re-cut them into Chapter 1 and parts of Chapter 2... because these "white papers" were older, they reflected Don's much more subjective Bayesian views of 10-15 years ago. I should have been more careful in editing out some of this stuff, because it's not the way he or I or any "working Bayesian" thinks any more... But this point of view was still feasible back then; see e.g. Jay Kadane's book for a purely subjective Bayes take (unsurprising given its author) on clinical trials.

Personally, I am of the Jaynesian school of thought which holds that if two agents have the same state of information, then they ought to assign the same probability distributions.