  QBism is an interpretation of quantum theory which views quantum mechanics as
standard probability theory supplemented with a few extra normative
constraints. The fundamental gambit is to represent states and measurements, as
well as time evolution, with respect to an informationally complete reference
device. From this point of view, the Born rule appears as a coherence condition
on probability assignments across several different experiments which manifests
as a deformation of the law of total probability (LTP). In this work, we fully
characterize those reference devices for which this deformation takes a
"simplest possible" (term-wise affine) form. Working in the framework of
generalized probability theories (GPTs), we show that, given any reference
measurement, a set of post-measurement reference states can always be chosen to
give its probability rule this very form. The essential condition is that the
corresponding measure-and-prepare channel be depolarizing. We also relate our
construction to Szymusiak and S{\l}omczy\'nski's recently introduced notion of
morphophoricity and re-examine critically a matrix-norm-based measure of LTP
deformation in light of our results. What stands out for the QBist project from
this analysis is that it is not only the pure form of the Born rule that must
be understood normatively, but the constants within it as well. It is they that
carry the details of quantum theory.
