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


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  • Bernard Monjardet

    (CES - Centre d'économie de la Sorbonne - CNRS : UMR8174 - Université Paris 1 - Panthéon-Sorbonne, CAMS - Centre d'analyse et de mathématique sociale - CNRS : UMR8557 - École des Hautes Études en Sciences Sociales (EHESS))


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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Bibliographic Info

Paper provided by HAL in its series Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) with number halshs-00309825.

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Date of creation: 2008
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Publication status: Published, Electronic Journal for History of Probability and Statistics, 2008, 4, 1, 1-26
Handle: RePEc:hal:cesptp:halshs-00309825

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Keywords: Condorcet's effect ; Fermat's point ; majority rule ; "Mathématique sociale" ; median algebra ; metric space ; permutohedron;

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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.


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