The wave-function as a true ensemble

In quantum mechanics, the wave-function only predicts probabilities of measurement outcomes, not individual outcomes. This suggests that it describes an ensemble of states with different values of a hidden variable. Here, we analyse this idea with reference to currently known theorems and experiments. We argue that the $psi$-ontic/epistemic distinction fails to properly identify ensemble interpretations and propose a more useful definition. We then show that all $psi$-ensemble interpretations which reproduce quantum mechanics violate Statistical Independence. Finally, we explain how this interpretation helps make sense of some otherwise puzzling phenomena in quantum mechanics, such as the delayed choice experiment, the Elitzur-Vaidman bomb detector, and the Extended Wigners Friends Scenario.