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Consensus among preference rankings: a new weighted correlation coefficient for linear and weak orderings

Author

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  • Antonella Plaia

    (University of Palermo)

  • Simona Buscemi

    (University of Palermo)

  • Mariangela Sciandra

    (University of Palermo)

Abstract

Preference 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.

Suggested Citation

  • Antonella Plaia & Simona Buscemi & Mariangela Sciandra, 2021. "Consensus among preference rankings: a new weighted correlation coefficient for linear and weak orderings," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 15(4), pages 1015-1037, December.
    • Handle: RePEc:spr:advdac:v:15:y:2021:i:4:d:10.1007_s11634-021-00442-x
    DOI: 10.1007/s11634-021-00442-x
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    References listed on IDEAS

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    1. Antonella Plaia & Mariangela Sciandra, 2019. "Weighted distance-based trees for ranking data," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 13(2), pages 427-444, June.
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    3. Antonio D’Ambrosio & Willem J. Heiser, 2016. "A Recursive Partitioning Method for the Prediction of Preference Rankings Based Upon Kemeny Distances," Psychometrika, Springer;The Psychometric Society, vol. 81(3), pages 774-794, September.
    4. Cook, Wade D., 2006. "Distance-based and ad hoc consensus models in ordinal preference ranking," European Journal of Operational Research, Elsevier, vol. 172(2), pages 369-385, July.
    5. Michael Fligner & Joseph Verducci, 1990. "Posterior probabilities for a consensus ordering," Psychometrika, Springer;The Psychometric Society, vol. 55(1), pages 53-63, March.
    6. Irurozki, Ekhine & Calvo, Borja & Lozano, Jose A., 2016. "PerMallows: An R Package for Mallows and Generalized Mallows Models," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 71(i12).
    7. Amodio, S. & D’Ambrosio, A. & Siciliano, R., 2016. "Accurate algorithms for identifying the median ranking when dealing with weak and partial rankings under the Kemeny axiomatic approach," European Journal of Operational Research, Elsevier, vol. 249(2), pages 667-676.
    8. Antonio D’Ambrosio & Carmela Iorio & Michele Staiano & Roberta Siciliano, 2019. "Median constrained bucket order rank aggregation," Computational Statistics, Springer, vol. 34(2), pages 787-802, June.
    9. Robert Fagot, 1994. "An ordinal coefficient of relational agreement for multiple judges," Psychometrika, Springer;The Psychometric Society, vol. 59(2), pages 241-251, June.
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    Cited by:

    1. Antonella Plaia & Simona Buscemi & Johannes Fürnkranz & Eneldo Loza Mencía, 2022. "Comparing Boosting and Bagging for Decision Trees of Rankings," Journal of Classification, Springer;The Classification Society, vol. 39(1), pages 78-99, March.
    2. Alessandro Albano & José Luis García-Lapresta & Antonella Plaia & Mariangela Sciandra, 2023. "A family of distances for preference–approvals," Annals of Operations Research, Springer, vol. 323(1), pages 1-29, April.

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