  In recent papers, Zurek has objected to the decision-theoretic approach of
Deutsch and Wallace to deriving the Born rule for quantum probabilities on the
grounds that it courts circularity. Deutsch and Wallace assume that the many
worlds theory is true and that decoherence gives rise to a preferred basis.
However, decoherence arguments use the reduced density matrix, which relies
upon the partial trace and hence upon the Born Rule for its validity. Using the
Heisenberg Picture and quantum Darwinism - the notion that classical
information is quantum information that can proliferate in the environment
pioneered by Olliver et al - I show that measurement interactions between two
systems only create correlations between a specific set of commuting
observables of system 1 and a specific set of commuting observables of system
2. This argument picks out a unique basis in which information flows in the
correlations between those sets of commuting observables. I then derive the
Born rule for both pure and mixed states and answer some other criticisms of
the decision theoretic approach to quantum probability.
