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

Bernard Monjardet

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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.

Keywords: Fermat's point; majority rule; "Mathématique sociale"; metric space; median algebra; Condorcet's effect; permutohedron; effet Condorcet; espace métrique; Mathématique sociale; médiane; permutoèdre; point de Fermat; règle majoritaire (search for similar items in EconPapers)
Date: 2008
Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-00309825
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Published in Electronic Journ@l for History of Probability and Statistics - Journal Electronique d'Histoire des Probabilités et de la Statistique, 2008, 4 (1), pp.1-26

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Working Paper: "Mathématique Sociale" and Mathematics. A case study: Condorcet's effect and medians (2008)
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