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A new position weight correlation coefficient for consensus ranking process without ties
Author(s) -
Plaia Antonella,
Buscemi Simona,
Sciandra Mariangela
Publication year - 2019
Publication title -
stat
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.61
H-Index - 18
ISSN - 2049-1573
DOI - 10.1002/sta4.236
Subject(s) - ranking (information retrieval) , rank (graph theory) , position (finance) , mathematics , preference , correlation coefficient , set (abstract data type) , rank correlation , correlation , combinatorics , statistics , computer science , artificial intelligence , geometry , finance , economics , programming language
Preference data represent a particular type of ranking data where a group of people give their preferences over a set of alternatives. The traditional metrics between rankings do not take into account the importance of swapping elements similar among them (element weights) or elements belonging to the top (or to the bottom) of an ordering (position weights). Following the structure of the τ x proposed by Emond and Mason and the class of weighted Kemeny–Snell distances, a proper rank correlation coefficient is defined for measuring the correlation among weighted position rankings without ties. The one‐to‐one correspondence between the weighted distance and the rank correlation coefficient holds, analytically speaking, using both equal and decreasing weights. In order to determine the consensus ranking among rankings, related to a set of subjects, the new coefficient is maximized modifying suitably a branch‐and‐bound algorithm proposed in literature.