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"Mathématique Sociale" and Mathematics. A case study: Condorcet's effect and medians

Author

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  • Bernard Monjardet

    () (CAMS - Centre d'analyse et de mathématique sociale - EHESS - École des hautes études en sciences sociales - CNRS - Centre National de la Recherche Scientifique, CES - Centre d'économie de la Sorbonne - UP1 - Université Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique)

Abstract

The "effet Condorcet" refers to the fact that the application of the pair-wise majority rule to individual preference orderings can generate a collective preference containing cycles. Condorcet's solution to deal with this disturbing fact has been recognized as the search for a median in a certain metric space. We describe the many areas of "applied" or "pure" mathematics where the notion of (metric) median has appeared. If it were actually necessary to give examples proving that "social mathematics" is mathematics, the median case would provide a convincing example.

Suggested Citation

  • Bernard Monjardet, 2008. ""Mathématique Sociale" and Mathematics. A case study: Condorcet's effect and medians," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00309825, HAL.
  • Handle: RePEc:hal:cesptp:halshs-00309825
    Note: View the original document on HAL open archive server: https://halshs.archives-ouvertes.fr/halshs-00309825
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    Cited by:

    1. Hudry, Olivier, 2012. "On the computation of median linear orders, of median complete preorders and of median weak orders," Mathematical Social Sciences, Elsevier, vol. 64(1), pages 2-10.
    2. Nehring, Klaus & Pivato, Marcus, 2018. "The median rule in judgement aggregation," MPRA Paper 84258, University Library of Munich, Germany.
    3. Pierluigi Contucci & Emanuele Panizzi & Federico Ricci-Tersenghi & Alina Sîrbu, 2016. "Egalitarianism in the rank aggregation problem: a new dimension for democracy," Quality & Quantity: International Journal of Methodology, Springer, vol. 50(3), pages 1185-1200, May.

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