  Using first principles from inference, we design a set of functionals for the
purposes of \textit{ranking} joint probability distributions with respect to
their correlations. Starting with a general functional, we impose its desired
behaviour through the \textit{Principle of Constant Correlations} (PCC), which
constrains the correlation functional to behave in a consistent way under
statistically independent inferential transformations. The PCC guides us in
choosing the appropriate design criteria for constructing the desired
functionals. Since the derivations depend on a choice of partitioning the
variable space into $n$ disjoint subspaces, the general functional we design is
the $n$-partite information (NPI), of which the \textit{total correlation} and
\textit{mutual information} are special cases. Thus, these functionals are
found to be uniquely capable of determining whether a certain class of
inferential transformations, $\rho\xrightarrow{*}\rho'$, preserve, destroy or
create correlations. This provides conceptual clarity by ruling out other
possible global correlation quantifiers. Finally, the derivation and results
allow us to quantify non-binary notions of statistical sufficency. Our results
express what percentage of the correlations are preserved under a given
inferential transformation or variable mapping.
