  Incomplete pairwise comparison matrices offer a natural way of expressing
preferences in decision making processes. Although ordinal information is
crucial, there is a bias in the literature: cardinal models dominate. Ordinal
models usually yield non-unique solutions; therefore, an approach blending
ordinal and cardinal information is needed. In this work, we consider two
cascading problems: first, we compute ordinal preferences, maximizing an index
that combines ordinal and cardinal information; then, we obtain a cardinal
ranking by enforcing ordinal constraints. Notably, we provide a sufficient
condition (that is likely to be satisfied in practical cases) for the first
problem to admit a unique solution and we develop a provably polynomial-time
algorithm to compute it. The effectiveness of the proposed method is analyzed
and compared with respect to other approaches and criteria at the state of the
art.
