  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 their values in a series of tests must conform with (2). The authority of von Neumann’s argument comes from the fact that requirements (1) and (2), for QM states, are consequences of the QM formalism, but this does not in itself justify extending these requirements to the hypothetical hidden states. Indeed, if (3) were unrestrictedly true, this would nicely explain, in the presence of hidden values, why (2) is. Von Neumann apparently thought that the HV proponent is committed to this explanation, but this seems an implausible restriction.