Pairwise ranking: choice of method can produce arbitrarily different rank order
Methodology
2011-03-08 v1 Numerical Analysis
Abstract
We examine three methods for ranking by pairwise comparison: Principal Eigenvector, HodgeRank and Tropical Eigenvector. It is shown that the choice of method can produce arbitrarily different rank order.To be precise, for any two of the three methods, and for any pair of rankings of at least four items, there exists a comparison matrix for the items such that the rankings found by the two methods are the prescribed ones. We discuss the implications of this result in practice, study the geometry of the methods, and state some open problems.
Keywords
Cite
@article{arxiv.1103.1110,
title = {Pairwise ranking: choice of method can produce arbitrarily different rank order},
author = {Ngoc Mai Tran},
journal= {arXiv preprint arXiv:1103.1110},
year = {2011}
}