An ideal Bayesian would employ the principle of maximum entropy for choosing priors [1], soon to discover the problem of underdetermination [2].
Such a person would suffer a death akin to Buridan's ass [3].
1. https://en.wikipedia.org/wiki/Principle_of_maximum_entropy
2. https://en.wikipedia.org/wiki/Underdetermination
3. https://en.wikipedia.org/wiki/Buridan%27s_ass