On strict ranking by pairwise comparisons
For researchers in decision-making and ranking, this provides a method to obtain strict rankings from pairwise comparisons, though the approach is incremental.
The paper addresses the problem of deriving a strict ranking (no ties) from a pairwise comparisons matrix. It proposes a heuristic based on the R-condition and a minimization problem that yields consistent pairwise comparisons producing a strict ranking.
We attack the problem of getting a strict ranking (i.e. a ranking without equally ranked items) of $n$ items from a pairwise comparisons matrix. Basic structures are described, a first heuristical approach based on a condition, the $\mathcal{R}-$condition, is proposed. Analyzing the limits of this ranking procedure, we finish with a minimization problem which can be applied to a wider class of pairwise comparisons matrices. If solved, it produces consistent pairwise comparisons that produce a strict ranking.