  We introduce a correlation coefficient that is designed to deal with a
variety of ranking formats including those containing non-strict (i.e.,
with-ties) and incomplete (i.e., unknown) preferences. The correlation
coefficient is designed to enforce a neutral treatment of incompleteness
whereby no assumptions are made about individual preferences involving unranked
objects. The new measure, which can be regarded as a generalization of the
seminal Kendall tau correlation coefficient, is proven to satisfy a set of
metric-like axioms and to be equivalent to a recently developed ranking
distance function associated with Kemeny aggregation. In an effort to further
unify and enhance both robust ranking methodologies, this work proves the
equivalence of an additional distance and correlation-coefficient pairing in
the space of non-strict incomplete rankings. These connections induce new exact
optimization methodologies: a specialized branch and bound algorithm and an
exact integer programming formulation. Moreover, the bridging of these
complementary theories reinforces the singular suitability of the featured
correlation coefficient to solve the general consensus ranking problem. The
latter premise is bolstered by an accompanying set of experiments on random
instances, which are generated via a herein developed sampling technique
connected with the classic Mallows distribution of ranking data. Associated
experiments with the branch and bound algorithm demonstrate that, as data
becomes noisier, the featured correlation coefficient yields relatively fewer
alternative optimal solutions and that the aggregate rankings tend to be closer
to an underlying ground truth shared by a majority.
