DrChinese said:
Unless I don't understand your comment, Bell precludes that.
There are no data sets or statistical averages for quantum spins independent of the measurement setting(s). Keeping in mind that there are a multitude of statistical requirements due to the multitude of possible settings (thinking of typical Bell tests here).
It's true that there's no sample space that is, even in principle, appropriate for all observables. But we can still build models that reference the values of observables before measurement. E.g. Take a typical EPRB experiment: Alice and Bob each have one of a pair of entangled particles. At time ##t_1## Alice measures her particle (particle a) in the basis ##|\uparrow_x^a\rangle,|\downarrow_x^a\rangle## and at the same time Bob measures his particle (particle b) in the basis ##|\uparrow_z^b\rangle,|\downarrow_z^b\rangle##. A typical sample space of outcomes for this experiment could be built from the projective decomposition of the identity on ##\mathcal{H}_{t_1}##
$$\begin{eqnarray*} I &=& |\uparrow_x^a,A_\uparrow,\uparrow_z^b,B_\uparrow\rangle\langle\uparrow_x^a,A_\uparrow,\uparrow_z^b,B_\uparrow|_{t_1} + \\
&& |\downarrow_x^a,A_\downarrow,\uparrow_z^b,B_\uparrow\rangle\langle\downarrow_x^a,A_\downarrow,\uparrow_z^b,B_\uparrow|_{t_1} + \\
&&|\uparrow_x^a,A_\uparrow,\downarrow_z^b,B_\downarrow\rangle\langle\uparrow_x^a,A_\uparrow,\downarrow_z^b,B_\downarrow|_{t_1} + \\
&& |\downarrow_x^a,A_\downarrow,\downarrow_z^b,B_\downarrow\rangle\langle\downarrow_x^a,A_\downarrow,\downarrow_z^b,B_\downarrow|_{t_1}
\end{eqnarray*}$$
where A and B are Alice and Bob's measuring devices respectively, and each of the four projectors above represents one of the four possible experimental outcomes.
But we could also construct an alternative model that includes statements about the spin of the particle at time ##t_0## before measurement. This times we consider the projective decomposition* of the identity on ##\mathcal{H}_{t_0}\otimes\mathcal{H}_{t_1}##
$$\begin{eqnarray*} I &=& |\uparrow_x^a,\uparrow_z^b\rangle\langle \uparrow_x^a,\uparrow_z^b|_{t_0}\otimes|\uparrow_x^a,A_\uparrow,\uparrow_z^b,B_\uparrow\rangle\langle\uparrow_x^a,A_\uparrow,\uparrow_z^b,B_\uparrow|_{t_1} + \\
&& |\downarrow_x^a,\uparrow_z^b\rangle\langle \downarrow_x^a,\uparrow_z^b|_{t_0}\otimes|\downarrow_x^a,A_\downarrow,\uparrow_z^b,B_\uparrow\rangle\langle\downarrow_x^a,A_\downarrow,\uparrow_z^b,B_\uparrow|_{t_1} + \\
&&|\uparrow_x^a,\downarrow_z^b\rangle\langle \uparrow_x^a,\downarrow_z^b|_{t_0}\otimes|\uparrow_x^a,A_\uparrow,\downarrow_z^b,B_\downarrow\rangle\langle\uparrow_x^a,A_\uparrow,\downarrow_z^b,B_\downarrow|_{t_1} + \\
&& |\downarrow_x^a,\downarrow_z^b\rangle\langle \downarrow_x^a,\downarrow_z^b|_{t_0}\otimes|\downarrow_x^a,A_\downarrow,\downarrow_z^b,B_\downarrow\rangle\langle\downarrow_x^a,A_\downarrow,\downarrow_z^b,B_\downarrow|_{t_1}
\end{eqnarray*}$$
Here, we model the measured properties at ##t_0## before the measurement has occurred. All the inferences from this model would be just as valid as from the previous model.
tl;dr The formalism doesn't seem to privilege properties after measurement over properties before measurement. Whether or not these properties are real, they seem to be just as real/not real before and after measurement.
*neglecting projections that would give zero probability, like ##|\downarrow_x^a,\uparrow_z^b\rangle\langle \downarrow_x^a,\uparrow_z^b|_{t_0}\otimes|\uparrow_x^a,A_\uparrow,\uparrow_z^b,B_\uparrow\rangle\langle\uparrow_x^a,A_\uparrow,\uparrow_z^b,B_\uparrow|_{t_1}##
