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Computing Kemeny Rankings from d-Euclidean Preferences

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Algorithmic Decision Theory (ADT 2021)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 13023))

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Abstract

Kemeny’s voting rule is a well-known and computationally intractable rank aggregation method. In this work, we propose an algorithm that finds an embeddable Kemeny ranking in d-Euclidean elections. This algorithm achieves a polynomial runtime (for a fixed dimension d) and thus demonstrates the algorithmic usefulness of the d-Euclidean restriction. We further investigate how well embeddable Kemeny rankings approximate optimal (unrestricted) Kemeny rankings.

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Notes

  1. 1.

    The geometric median of a set of points S is a point that minimizes the sum of distances to points in S (as does the Kemeny ranking albeit for a different metric).

  2. 2.

    We construct the preference graph \(H_{\mathrm {pref}}\) by adapting the dual arrangement construction from CGAL (The CGAL Project, https://www.cgal.org) and apply Johnson’s all-pairs shortest path algorithm to determine the p-embeddable Kemeny rankings.

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Acknowledgments

This work was supported by the Austrian Science Foundation FWF through projects P31890, P31336, W1255-N23, and Y1329.

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Correspondence to Thekla Hamm .

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Hamm, T., Lackner, M., Rapberger, A. (2021). Computing Kemeny Rankings from d-Euclidean Preferences. In: Fotakis, D., Ríos Insua, D. (eds) Algorithmic Decision Theory. ADT 2021. Lecture Notes in Computer Science(), vol 13023. Springer, Cham. https://doi.org/10.1007/978-3-030-87756-9_10

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  • DOI: https://doi.org/10.1007/978-3-030-87756-9_10

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