  The objective of the consistent-amplitude approach to quantum theory has been
to justify the mathematical formalism on the basis of three main assumptions:
the first defines the subject matter, the second introduces amplitudes as the
tools for quantitative reasoning, and the third is an interpretative rule that
provides the link to the prediction of experimental outcomes. In this work we
introduce a natural and compelling fourth assumption: if there is no reason to
prefer one region of the configuration space over another then they should be
`weighted' equally. This is the last ingredient necessary to introduce a unique
inner product in the linear space of wave functions. Thus, a form of the
principle of insufficient reason is implicit in the Hilbert inner product.
Armed with the inner product we obtain two results. First, we elaborate on an
earlier proof of the Born probability rule. The implicit appeal to insufficient
reason shows that quantum probabilities are not more objective than classical
probabilities. Previously we had argued that the consistent manipulation of
amplitudes leads to a linear time evolution; our second result is that time
evolution must also be unitary. The argument is straightforward and hinges on
the conservation of entropy. The only subtlety consists of defining the correct
entropy; it is the array entropy, not von Neumann's. After unitary evolution
has been established we proceed to introduce the useful notion of observables
and we explore how von Neumann's entropy can be linked to Shannon's information
theory. Finally, we discuss how various connections among the postulates of
quantum theory are made explicit within this approach.
