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

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  • Bernard Monjardet

    (CAMS - Centre d'Analyse et de Mathématique sociales - EHESS - École des hautes études en sciences sociales - CNRS - Centre National de la Recherche Scientifique, CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 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.

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  • Bernard Monjardet, 2008. ""Mathématique Sociale" and Mathematics. A case study: Condorcet's effect and medians," Post-Print halshs-00309825, HAL.
    • Handle: RePEc:hal:journl:halshs-00309825
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-00309825
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    References listed on IDEAS

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    1. 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.
    2. Bernard Monjardet, 2009. "Acyclic Domains of Linear Orders: A Survey," Studies in Choice and Welfare, in: Steven J. Brams & William V. Gehrlein & Fred S. Roberts (ed.), The Mathematics of Preference, Choice and Order, pages 139-160, Springer.
    3. Ádám Galambos & Victor Reiner, 2008. "Acyclic sets of linear orders via the Bruhat orders," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 30(2), pages 245-264, February.
    4. Pierre Barthelemy, Jean & Monjardet, Bernard, 1981. "The median procedure in cluster analysis and social choice theory," Mathematical Social Sciences, Elsevier, vol. 1(3), pages 235-267, May.
    5. Lawrence M. Ostresh, 1978. "Convergence and Descent in the Fermat Location Problem," Transportation Science, INFORMS, vol. 12(2), pages 153-164, May.
    6. Galina Jalal & Jakob Krarup, 2003. "Geometrical Solution to the Fermat Problem with Arbitrary Weights," Annals of Operations Research, Springer, vol. 123(1), pages 67-104, October.
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    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. Klaus Nehring & Marcus Pivato, 2022. "The median rule in judgement aggregation," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 73(4), pages 1051-1100, June.

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