This study demonstrates that incorrect data are entered into a pairwise comparisons matrix for processing into weights for the data collected by a rating scale. Unprocessed rating scale data lead to a paradox. A solution to it, based on normalization, is proposed. This is an essential correction for virtually all pairwise comparisons methods using rating scales. The illustration of the relative...

In this paper we propose a full Bayesian probabilistic method to learn preferences from non-transitive pairwise comparison data. Such lack of transitivity easily arises when the number of pairwise comparisons is large, and they are given sequentially without allowing for consistency check. We develop a Bayesian Mallows model able to handle such data through a latent layer of uncertainty which c...

A common problem in machine learning is to rank a set of n items based on pairwise comparisons. Here ranking refers to partitioning the items into sets of pre-specified sizes according to their scores, which includes identification of the top-k items as the most prominent special case. The score of a given item is defined as the probability that it beats a randomly chosen other item. Finding an...