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

Author

Listed:
  • Francisco Pedroche

    (Institut de Matemàtica Multidisciplinària, Universitat Politècnica de València, Camí de Vera s/n, 46022 València, Spain)

  • J. Alberto Conejero

    (Instituto Universitario de Matemática Pura y Aplicada, Universitat Politècnica de València, Camí de Vera s/n, 46022 València, Spain)

Abstract

Mathematical analysis of rankings is essential for a wide range of scientific, public, and industrial applications (e.g., group decision-making, organizational methods, R&D sponsorship, recommender systems, voter systems, sports competitions, grant proposals rankings, web searchers, Internet streaming-on-demand media providers, etc.). Recently, some methods for incomplete aggregate rankings (rankings in which not all the elements are ranked) with ties, based on the classic Kendall’s tau coefficient, have been presented. We are interested in ordinal rankings (that is, we can order the elements to be the first, the second, etc.) allowing ties between the elements (e.g., two elements may be in the first position). We extend a previous coefficient for comparing a series of complete rankings with ties to two new coefficients for comparing a series of incomplete rankings with ties. We make use of the newest definitions of Kendall’s tau extensions. We also offer a theoretical result to interpret these coefficients in terms of the type of interactions that the elements of two consecutive rankings may show (e.g., they preserve their positions, cross their positions, and they are tied in one ranking but untied in the other ranking, etc.). We give some small examples to illustrate all the newly presented parameters and coefficients. We also apply our coefficients to compare some series of Spotify charts, both Top 200 and Viral 50, showing the applicability and utility of the proposed measures.

Suggested Citation

  • Francisco Pedroche & J. Alberto Conejero, 2020. "Corrected Evolutive Kendall’s τ Coefficients for Incomplete Rankings with Ties: Application to Case of Spotify Lists," Mathematics, MDPI, vol. 8(10), pages 1-30, October.
  • Handle: RePEc:gam:jmathe:v:8:y:2020:i:10:p:1828-:d:430722
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    References listed on IDEAS

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    1. Luis Aguiar & Joel Waldfogel, 2018. "Platforms, Promotion, and Product Discovery: Evidence from Spotify Playlists," JRC Working Papers on Digital Economy 2018-04, Joint Research Centre.
    2. Erick Moreno-Centeno & Adolfo R. Escobedo, 2016. "Axiomatic aggregation of incomplete rankings," IISE Transactions, Taylor & Francis Journals, vol. 48(6), pages 475-488, June.
    3. William Redman, 2019. "An O(n) method of calculating Kendall correlations of spike trains," PLOS ONE, Public Library of Science, vol. 14(2), pages 1-7, February.
    4. Yoo, Yeawon & Escobedo, Adolfo R. & Skolfield, J. Kyle, 2020. "A new correlation coefficient for comparing and aggregating non-strict and incomplete rankings," European Journal of Operational Research, Elsevier, vol. 285(3), pages 1025-1041.
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