On strict ranking by pairwise comparisons

TL;DR

This paper explores methods for deriving strict rankings from pairwise comparison matrices, introducing a heuristic and a minimization approach to improve ranking consistency.

Contribution

It proposes a new heuristic based on the r-condition and a minimization framework for producing consistent, strict rankings from pairwise comparison data.

Findings

The r-condition heuristic offers a practical ranking method.

The minimization problem can generate consistent comparison matrices.

The approaches extend to broader classes of pairwise comparison matrices.

Abstract

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.