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A formalization of consensus index methods

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Abstract

A consensus in dex method comprises a consensus method and a consensus index that are defined on a common set of objects (e.g. classifications). For each profile of objects, the consensus method returns a consensus object representing information or structure shared among profile objects, while the consensus index returns a quantitative measure of agreement among profile objects. Since the relationship between consensus method and consensus index is poorly understood, we propose simple axioms prescribing it in the most general terms. Many taxonomic consensus index methods violate these axioms because their consensus indices measure consensus object invariants rather than profile agreement. We propose paradigms to obtain consensus index methods that measure agreement and satisfy the axioms. These paradigms salvage concepts underlying consensus index methods violating the axioms.

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Authors and Affiliations

  1. Department of Computer Science, Memorial University of Newfoundland, A1C 5S7, St. John's, New foundland, Canada

    William H. E. Day

  2. Department of Mathematics, University of Louisville, 40292, Louisville, KY, USA

    F. R. McMorris

Authors
  1. William H. E. Day
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  2. F. R. McMorris
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Additional information

This work was supported in part by the Faculty of Science at Memorial University of Newfoundland, and by the Natural Sciences and Engineering Research Council of Canada Under Grant A-4142.

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Day, W.H.E., McMorris, F.R. A formalization of consensus index methods. Bltn Mathcal Biology 47, 215–229 (1985). https://doi.org/10.1007/BF02460032

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  • DOI: https://doi.org/10.1007/BF02460032

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