Quantum Bayesianism and Bayesianism I am studying both Quantum Bayesianism (QBism) and Bayesianism (the idea that probability is subjective). I am wondering if QBism and Bayesianism face the same objections and lead to the same problems inherently to probability. Moreover, in what they differ in the treatment of probability? And what are the similar problems they share? While what problems are different between the two?
 A: It is almost universally accepted among statisticians these days that probabilities are always Bayesian. That is to say they quantify the human assessment of knowledge. This was actually always the interpretation of probability theory except for a short period in the first half of the last century when frequentism became fashionable in an attempt to see probability as abstracted from reality. For example Maxwell wrote 

“The actual science of logic is conversant at present only with things either certain,
  impossible, or entirely doubtful, none of which (fortunately) we have to reason
  on. Therefore the true logic for this world is the calculus of Probabilities,
  which takes account of the magnitude of the probability which is, or ought to be,
  in a reasonable man’s mind.” (James Clerk Maxwell (ed. P. M. Harman), 1990, The Scientific Letters and Papers of James Clerk Maxwell, Vol. 1, 1846-1862, p.197, CUP Press).

Ultimately it was recognised that the limiting procedures used in frequentism are not present in reality, but only "in a reasonable man's mind", and that frequentism was misguided. However, frequentism was fashionable at the time when von Neumann and Dirac formulated quantum mechanics as a probability theory, and motivates von Neumann's discussion of "ensembles".
Take away frequentism, and Quantum Bayesianism is really just the orthodox (Dirac-von Neumann) interpretation of quantum mechanics dressed up in new clothes. This is a distinction without a difference. All QB says is that quantum mechanics is a probability theory, which we already know. It singularly fails to address the underlying question, examined, and already answered, by von Neumann (albeit in almost unintelligible language). That is to say, why do probabilities in quantum mechanics follow different rules for calculation than the rules we are familiar with in classical probability theory? 
The difference is that in quantum mechanics probabilities apply to the case where results are actually indeterminate, not to the case where they are determined by unknown quantities. This was shown by von Neumann, and is the basis of the Dirac-von Neumann form of the Copenhagen interpretation (which does not include wave particle duality -- waves are probability amplitudes and exist in mathematics, not in reality).
The main difference is that while von Neumann used mathematics, others, like Fuchs, have only hand wavy arguments. I would say the same of others, like Saul Youssef’s interpretation that quantum mechanics is an “exotic probability theory”, or a host of so called “information theoretic interpretations”.
To count as interpretation, one must explicitly relate the interpretation to mathematical structure, and demonstrate why the mathematical structure necessitates the Schrodinger equation. I have clarified the Dirac-von Neumann interpretation and shown this in a Bayesian context in a published paper The Hilbert space of conditional clauses
