I remember vaguely one discussion of Bayesianism vs. frequentism, where the frequentists held that a study in which the experimenters resolved to keep making observations until they observed Foo X times (for a total of X times and Y total observations) must be treated statistically different from a study where the experimenters resolved to make Y total observations but wound up X times observing Foo; while from the Bayesian perspective, these studies, with their identical objective facts, ought to be treated the same.

Does this sound like it?