Ranking by pairwise comparisons for Swiss-system tournaments

TL;DR

This paper introduces a novel ranking method for Swiss-system tournaments using incomplete pairwise comparison matrices, incorporating a distance function to compare rankings and visualizing results with Multidimensional Scaling, showing improved outcomes over traditional methods.

Contribution

It proposes a new ranking approach based on pairwise comparisons and a distance measure, applied to chess tournaments, with visualization and robustness analysis.

Findings

Results are robust to scaling techniques.

Proposed rankings sometimes outperform traditional lexicographical orders.

Visualization aids in understanding ranking differences.

Abstract

Pairwise comparison matrices are widely used in Multicriteria Decision Making. This article applies incomplete pairwise comparison matrices in the area of sport tournaments, namely proposing alternative rankings for the 2010 Chess Olympiad Open tournament. It is shown that results are robust regarding scaling technique. In order to compare different rankings, a distance function is introduced with the aim of taking into account the subjective nature of human perception. Analysis of the weight vectors implies that methods based on pairwise comparisons have common roots. Visualization of the results is provided by Multidimensional Scaling on the basis of the defined distance. The proposed rankings give in some cases intuitively better outcome than currently used lexicographical orders.