6533b82ffe1ef96bd1295317
RESEARCH PRODUCT
Consensus among preference rankings: a new weighted correlation coefficient for linear and weak orderings
Antonella PlaiaSimona BuscemiMariangela Sciandrasubject
Statistics and ProbabilityClass (set theory)Correlation coefficientApplied Mathematics02 engineering and technologyType (model theory)01 natural sciencesComputer Science ApplicationsSet (abstract data type)010104 statistics & probabilityRankingPosition (vector)StatisticsWeighted Rank correlation coefficient Weighted Kemeny distance Position weightsTies0202 electrical engineering electronic engineering information engineering020201 artificial intelligence & image processing0101 mathematicsSettore SECS-S/01 - StatisticaPreference (economics)MathematicsRank correlationdescription
AbstractPreference data are a particular type of ranking data where some subjects (voters, judges,...) express their preferences over a set of alternatives (items). In most real life cases, some items receive the same preference by a judge, thus giving rise to a ranking with ties. An important issue involving rankings concerns the aggregation of the preferences into a “consensus”. The purpose of this paper is to investigate the consensus between rankings with ties, taking into account the importance of swapping elements belonging to the top (or to the bottom) of the ordering (position weights). By combining the structure of $$\tau _x$$ τ x proposed by Emond and Mason (J Multi-Criteria Decis Anal 11(1):17–28, 2002) with the class of weighted Kemeny-Snell distances, a position weighted rank correlation coefficient is proposed for comparing rankings with ties. The one-to-one correspondence between the weighted distance and the rank correlation coefficient is proved, analytically speaking, using both equal and decreasing weights.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2021-05-28 | Advances in Data Analysis and Classification |