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Guilbaud's 1952 theorem on the logical problem of aggregation

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In a paper published in 1952, shortly after publication of Arrow's celebrated impossibility result, the French mathematicien Georges-Théodule Guilbaud has obtained a dictatorship result for the logical problem of aggregation, thus anticipating the literature on abstract aggregation theory and judgment aggregation. We reconstruct the proof of Guilbaud's theorem, which is also of technical interest, because it can be seen as the first use of ultrafilters in social choice theory

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  • Daniel Eckert & Bernard Monjardet, 2010. "Guilbaud's 1952 theorem on the logical problem of aggregation," Documents de travail du Centre d'Economie de la Sorbonne 10056, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    • Handle: RePEc:mse:cesdoc:10056
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    1. Herzberg, Frederik S., 2008. "Judgement aggregation functions and ultraproducts," MPRA Paper 10546, University Library of Munich, Germany, revised 10 Sep 2008.
    2. Donald J. Brown, 1975. "Aggregation of Preferences," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 89(3), pages 456-469.
    3. Bernard Monjardet, 2005. "Social choice theory and the “Centre de Mathématique Sociale”: some historical notes," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 25(2), pages 433-456, December.
    4. Bengt Hansson, 1976. "The existence of group preference functions," Public Choice, Springer, vol. 28(1), pages 89-98, December.
    5. Barnett,William A. & Moulin,Hervé & Salles,Maurice & Schofield,Norman J. (ed.), 1995. "Social Choice, Welfare, and Ethics," Cambridge Books, Cambridge University Press, number 9780521443401.
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    Keywords

    Aggregation; judgment aggregation; logical connectives; simple game; ultrafilter;
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