It's well known that in quantum mechanics, a generic mixed state can be decomposed into pure states in infinitely many different ways.
While this property is kind of understandable if quantum states are viewed more like probability functions, it is kind of mysterious why it should be so in MWI.
Why is it so philosophically? It would seem more likely from an a priori philosophical standpoint that for MWI, different classical probability distributions over ontologically real wavefunctions ought to be empirically distinguishable. But yet, that's not the case if they end up with the same mixed density state.