  This paper defines a new pseudometric for binary relations between finite
sets that measures consensus among subsets. The main results are (1) a concise
restatement of this pseudometric with an intuitively appealing interpretation
via a full and faithful functor from the category of relations to a category of
relation multisets and (2) that the pseudometric can be bounded without an
expensive search of possible mappings, based solely on the dimensions of the
relations themselves. Additionally, (3) an algorithm is described to calculate
this bound with time and memory complexity at worst proportional to the product
of those dimensions: $\mathcal{O}(m \times n).$. The tools developed in this
paper should find broad application in exploratory data analysis. We provide
one such application by briefly exploring ad hoc consensus specifications for
the well-known PDF file format.
