  We address the question of whether the quantum-mechanical wave function
$\Psi$ of a system is uniquely determined by any complete description $\Lambda$
of 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 of
$\Lambda$. An implication of this result is that, among all possible
descriptions $\Lambda$ of a system's state compatible with free choice, the
wave function $\Psi$ is as objective as $\Lambda$.
