In this section we will show that the SVM, applied to ranking (as described in Section 3) has an O(n) sample complexity. A related claim (without complete proof) has been made in (Radinsky & Ailon, 2011). We then show that this sample complexity is tight. Proposition 3.1. There is a constant d, so that for any 0 < η < 1, if we noiselessly measure dn/η binary comparisons, chosen uniformly at ran...

A new approach to Pairwise Comparisons based Ranking is presented. An abstract model based on partial orders instead of numerical scales is introduced and analysed. The importance of the concept of indifference and the power of weak order extensions are discussed.

Inconsistency in pairwise comparison judgements is often perceived as an unwanted phenomenon and researchers have proposed a number of techniques to either reduce it or correct it. We take viewpoint that this inconsistency unleashes different mindsets the decision maker(s) should be taken into account when generating recommendations support. With aim we consider spanning trees analysis which re...

To analyse paired comparison outcomes, such as with non-standard probabilities, a basis is created for the space of all binary interactions, whether from probabilities, correlations, etc. In this manner, the source of all transitive and non-transitive behaviours (e.g. path dependencies) can be identified.