We address the question of whether the quantum-mechanical wave functionΨof a system is uniquely determined by any complete descriptionΛof the system’s physical state. We show that this is the case if the latter satisfies a notion of‘free choice’. This notion requires that certain experimental parameters—those that according to quantum theory can be chosen independently of other variables—retain this property in the presence ofΛ. An implication of this result is that, among all possible descriptionsΛof a system’s state compatible with free choice, the wave function Y is as objective asΛ.