A new correlation coefficient for comparing and aggregating non-strict and incomplete rankings

Corrected Evolutive Kendall’s τ Coefficients for Incomplete Rankings with Ties: Application to Case of Spotify Lists

“…For example, in [10] the term partial is used to indicate rankings in which ties are presented, while in [11] the term partial indicates that not all the objects are compared. In this paper, we use the terminology coined in [4,12]. We talk of complete rankings when all the objects are compared (as in a football league) and incomplete when there are absent objects (as in a Top k ranking).…”

“…More recently, in [4] these previous works were revised and a new axiomatic framework for incomplete rankings was introduced. To the best of our knowledge, the last paper devoted to an axiomatic study for incomplete rankings is [12], where it is shown as an extension of Kendall's τ coefficient to the case of incomplete rankings with ties.…”

“…Kendall's τ has been extensively used, and some extensions can be found in the literature up to the present day on [10,12,20]. In particular, Kendall's τ has been recently reviewed for ophthalmic research in [21] and it is a tool used in neuroscience studies-e.g., [22]-and in bioinformatics [23].…”

“…In this paper, we take some results of [4,12] as our starting point to develop two coefficients to describe the evolution of a series of m ≥ 2 incomplete rankings with ties. When applied to the case of only two rankings, our measures reduce to the measures given in [4,12].…”

“…We also extend the study of a series of complete rankings with ties developed in [13] to the case of incomplete rankings with ties. We make use of the standard modern notation in the field of rankings mainly based on [10,12,27], among others.…”