Quantum Completeness and Derivations of the Born Rule

No-hidden-variables proofs of Kochen-Specker type show that quantum mechanics (QM) cannot be complemented by hidden variables in the following sense. Specific sets of observables on a system S do not permit the simultaneous ascription of (non-contextual, functional-relation-respecting) values. This is generally interpreted as showing that one direction of the eigenstate-eigenvalue link is true. If S is in a (pure) state |b>| ak > (where A | ak > = ak | ak > for an operator A), then S does not have the value ak of A. (Call this assumption Completeness.) But Completeness is in disharmony with QM itself, in a reasonably axiomatized version. Indeed, given two very general principles about probabilities QM and Completeness generate a contradiction. (Call this contradiction the Completeness Problem.)
The Completeness Problem and the two principles have been discussed extensively elsewhere (see arxiv.org/abs/0705.2763 and Found. Phys. 38: 707-732, (2008)). At heart, the problem is a conflict between the Born Rule and Completeness. (The other axioms and the principles have ancillary character for the argument.) This raises a number of questions. Notably, it is basic to the argument that the Born Rule is seen as an essential and independent axiom of QM; then Completeness is seen to be an incoherent addition to QM. However, other theoreticians claim to be able to derive the Born Rule from QM plus other assumptions - sometimes including Completeness. Are these derivation attempts defective or is the Completeness Problem spurious? Is the Born Rule an independent axiom of QM, in the first place? In the talk, I will try to answer these questions, concentrating on Zurek's derivation proposal (arxiv.org/abs/quant-ph/0211037 Phys. Rev. Lett. 90, 120403 (2003)). I will show that Zurek does not derive, but presuppose the crucial portion of the Born Rule - the encoding of non-trivial probabilities in the state. From this portion alone, the Completeness Problem can be generated. Since Zurek also accepts completeness, the consistency of his approach is called into doubt. Time permitting I will also consider the Deutsch-Wallace proposal for deriving the Born Rule from decision-theoretic assumptions.