Requirements (1) and (2) being consequences of the QM formalism for QM states does not justify extending these requirements to hypothetical hidden states.

The example illustrates why von Neumann’s argument is unsatisfying. Nobody disputes the move from (2) to (3) for compatible observables, i.e. those which, according to QM, are jointly measurable in one arrangement. The above choice of A, B, C, however, is such that any two of them are incompatible, i.e. are not jointly observable. For these we will not want to require any HV interpretation to meet (3), but only (2). The hidden values need not conform with (3) in general, only the averages of the