Median constrained bucket order rank aggregation

Abstract

The rank aggregation problem can be summarized as the problem of aggregating individual preferences expressed by a set of judges to obtain a ranking that represents the best synthesis of their choices. Several approaches for handling this problem have been proposed and are generally linked with either axiomatic frameworks or alternative strategies. In this paper, we present a new definition of median ranking and frame it within the Kemeny’s axiomatic framework. Moreover, we show the usefulness of our approach in a practical case about triage prioritization.

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Notes

  1. 1.

    The first axiom states that the distance measure must be a metric. The second axiom is about the invariance of the distance under a random permutations of the items. The third axiom is about consistency in measurement: the distance between two rankings does not change after deleting a set of items that agrees in rank for both rankings. The last axiom is the statement of a measurement unit: the minimum distance is equal to one.

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Acknowledgements

The authors would like to thank Prof. Dr. Giuseppe Zollo and Dr. Lorella Cannavacciuolo of the University of Naples Federico II for kindly providing us the triage dataset. The authors would also like to thank both the Editor and the two anonymous reviewers, whose comments highly contributed to improving the quality of the manuscript.

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Correspondence to Antonio D’Ambrosio.

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This work has been partially supported by the H2020-EU.3.5.4. Project ‘Moving Towards Adaptive Governance in Complexity: Informing Nexus Security (MAGIC)’, Grant Agreement Number 689669.

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D’Ambrosio, A., Iorio, C., Staiano, M. et al. Median constrained bucket order rank aggregation. Comput Stat 34, 787–802 (2019). https://doi.org/10.1007/s00180-018-0858-z

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Keywords

  • Tied rankings
  • Median ranking
  • Kemeny distance
  • Triage prioritization