The existence of persistent disagreements is a puzzle from a Bayesian
perspective. If there is only one reality, and everyone can talk to each other,
then we should converge on the right answer^{1}.

That persistent disagreements exist is (perhaps) an argument against the Bayesian perspective. At least the philosophy, I don’t know if there is some great bearing on statistical practice.

On the other hand, Bayesians have tools that let others take the evidence contained in the data, then properly and simply apply the user’s own prior distributions. I’m thinking in particular about Bayes Factors, which can be easily re-weighted when the prior changes, or when you give your work to someone with a different prior.

Relevant post from LessWrong: https://www.lesswrong.com/posts/8cWMX6L8St8k9pPRC/comment-on-endogenous-epistemic-factionalization↩