Bozóki, Sándor
(MTA SZTAKI)
Weighting and ranking based on
pairwise comparisons
Pairwise comparisons form a
basis of preference modeling and decision analysis with a wide range of
applications in multiple criteria decision making, group decision making,
ranking and voting.
A specific model of
pairwise comparisons, proposed by Saaty in 1977, is
discussed in the talk. A pairwise comparison matrix is built up from numerical
answers on questions like ‘How many times criterion i
is more important than criterion j?’ or ‘How many times action i is better than action j?’. The problem of weighting is
then to find a vector such that the pairwise ratios of its coordinates are as
close as possible to the corresponding matrix elements. The eigenvector, the
least squares and the logarithmic least squares methods are classical ways of
weighting, besides dozens of other proposals.
Incomplete pairwise
comparison matrices offer the possibility of ignoring some (in certain
applications more than 90%) of all the possible pairs in the questionnaire. Due
to this reduction, essentially larger weighting and ranking problems can be
considered and solved. For example, we recently developed a ranking method of
top tennis players.
The Pareto optimality of a
weight vector, derived from a pairwise comparison matrix, is a natural and
desirable property. A weight vector is called Pareto optimal if no other weight
vector is at least as good in approximating the elements of the pairwise
comparison matrix, and strictly better in at least one position. The least
squares method and the logarithmic least squares method always yield efficient
weight vectors, while the principal right eigenvector can be inefficient. It is
still open to find a necessary and sufficient condition for the Pareto optimality
of the eigenvector.
Main references
Bozóki, S., Fülöp,
J. (2017): Efficient weight vectors from pairwise comparison matrices, European
Journal of Operational Research, online first, DOI 10.1016/j.ejor.2017.06.033
Bozóki, S., Csató,
L., Temesi, J. (2016): An application of incomplete
pairwise comparison matrices for ranking top tennis players, European Journal
of Operational Research, 248(1), 211–218, with an online appendix at
http://www.sztaki.hu/%7Ebozoki/tennis/appendix.pdf
Bozóki, S., Fülöp,
J., Rónyai, L. (2010): On optimal completions of
incomplete pairwise comparison matrices, Mathematical and Computer Modelling,
52(1-2), 318–333
The talk is held in Hungarian!
Az előadás magyar nyelven lesz megtartva!
Date: Oct 31, Tuesday 4:15pm
Place: BME, Building „Q”, Room QBF13