  The study of ordering polytopes has been essential to the solution of various
challenging combinatorial optimization problems. For instance, the
incorporation of facet defining inequalities (FDIs) from these polytopes in
branch-and-cut approaches represents among the most effective solution
methodologies known to date for some of these problems. The weak order
polytope, defined as the convex hull of the characteristic vectors of all
binary orders on $n$ alternatives that are reflexive, transitive, and complete,
has been particularly important for tackling problems in computational social
choice, preference aggregation, and comparative probability. For the most part,
FDIs for the weak order polytope have been obtained through enumeration and
through derivation from FDIs of other combinatorial polytopes. This paper
derives new classes of FDIs for the weak order polytope by utilizing the
equivalent representation of a weak order as a ranking of $n$ objects that
allows ties and by grouping characteristic vectors that share certain ranking
structures. Furthermore, we demonstrate that a number of FDIs previously
obtained through enumeration are actually special cases of these ranking-based
FDIs.
