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Metric and latticial medians

Author

Listed:
  • Bernard Monjardet

    (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique)

  • Jean-Pierre Barthélemy

    (LUSSI - Département Logique des Usages, Sciences sociales et Sciences de l'Information - UEB - Université européenne de Bretagne - European University of Brittany - Télécom Bretagne - IMT - Institut Mines-Télécom [Paris])

  • Olivier Hudry

    (TSP - INF - Département Informatique - TSP - Télécom SudParis - IMT - Institut Mines-Télécom [Paris] - IP Paris - Institut Polytechnique de Paris)

  • Bruno Leclerc

    (CAMS - Centre d'Analyse et de Mathématique sociales - EHESS - École des hautes études en sciences sociales - CNRS - Centre National de la Recherche Scientifique)

Abstract

This paper presents the -linked- notions of metric and latticial medians and it explains what is the median procedure for the consensus problems, in particular in the case of the aggregation of linear orders. First we consider the medians of a v-tuple of arbitrary or particular binary relations.. Then we study in depth the difficult (in fact NP-difficult) problem of finding the median orders of a profile of linear orders. More generally, we consider the medians of v-tuples of elements of a semilattice and we describe the median semilattices, i.e. the semilattices were medians are easily computable.

Suggested Citation

  • Bernard Monjardet & Jean-Pierre Barthélemy & Olivier Hudry & Bruno Leclerc, 2009. "Metric and latticial medians," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00408174, HAL.
    • Handle: RePEc:hal:cesptp:halshs-00408174
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-00408174v1
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    Cited by:

    1. Irène Charon & Olivier Hudry, 2010. "An updated survey on the linear ordering problem for weighted or unweighted tournaments," Annals of Operations Research, Springer, vol. 175(1), pages 107-158, March.
    2. Olivier Hudry, 2015. "Complexity results for extensions of median orders to different types of remoteness," Annals of Operations Research, Springer, vol. 225(1), pages 111-123, February.
    3. Daniel Eckert & Bernard Monjardet, 2009. "Guilbaud's Theorem : An early contribution to judgment aggregation," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00404185, HAL.
    4. Ernesto Savaglio & Stefano Vannucci, 2022. "Strategy-proof aggregation rules in median semilattices with applications to preference aggregation," Papers 2208.12732, arXiv.org.

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