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Médianes métriques et latticielles

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Listed:
  • Olivier Hudry

    (ENST - Ecole Nationale Supérieure des Télécommunications)

  • 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)

  • Bernard Monjardet

    (CERMSEM - CEntre de Recherche en Mathématiques, Statistique et Économie Mathématique - 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])

Abstract

In this paper, we present the notion of median useful for the aggregation of preferences and, more generally, in problems of consensus. After the introduction on the general notion of median, the first section studies the median relations of a profile of arbitrary or particular (tournaments, linear orders) relations. The computation of the medians of linear orders is difficult. The second section is devoted to this problem of which several equivalent formulations are presented. Then complexity results are specified, resolution methods are sketched and properties of median linear orders are given. The third section bears on the case where the computation of medians is easy, i.e. the case where the set of objects to aggregate can be endowed with an order structure, namely a structure of median semilattice.

Suggested Citation

  • Olivier Hudry & Bruno Leclerc & Bernard Monjardet & Jean-Pierre Barthélemy, 2004. "Médianes métriques et latticielles," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-03322636, HAL.
    • Handle: RePEc:hal:cesptp:halshs-03322636
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-03322636v1
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    References listed on IDEAS

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    1. Bernard Monjardet, 2008. ""Mathématique Sociale" and Mathematics. A case study: Condorcet's effect and medians," Post-Print halshs-00309825, HAL.

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