  We describe a general procedure for associating a minimal
informationally-complete quantum measurement (or MIC) and a set of linearly
independent post-measurement quantum states with a purely probabilistic
representation of the Born Rule. Such representations are motivated by QBism,
where the Born Rule is understood as a consistency condition between
probabilities assigned to the outcomes of one experiment in terms of the
probabilities assigned to the outcomes of other experiments. In this setting,
the difference between quantum and classical physics is the way their physical
assumptions augment bare probability theory: Classical physics corresponds to a
trivial augmentation -- one just applies the Law of Total Probability (LTP)
between the scenarios -- while quantum theory makes use of the Born Rule
expressed in one or another of the forms of our general procedure. To mark the
irreducible difference between quantum and classical, one should seek the
representations that minimize the disparity between the expressions. We prove
that the representation of the Born Rule obtained from a symmetric
informationally-complete measurement (or SIC) minimizes this distinction in at
least two senses -- the first to do with unitarily invariant distance measures
between the rules, and the second to do with available volume in a reference
probability simplex (roughly speaking a new kind of uncertainty principle).
Both of these arise from a significant majorization result. This work
complements recent studies in quantum computation where the deviation of the
Born Rule from the LTP is measured in terms of negativity of Wigner functions.
