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Guilbaud's Theorem: an early contribution to judgment aggregation

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Abstract

In a paper published in 1952, the French matematician Georges-Théodule Guilbaud has generalized Arrow's impossibility result to 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, 2009. "Guilbaud's Theorem: an early contribution to judgment aggregation," Documents de travail du Centre d'Economie de la Sorbonne 09047, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    • Handle: RePEc:mse:cesdoc:09047
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    1. Blau, Julian H., 1979. "Semiorders and collective choice," Journal of Economic Theory, Elsevier, vol. 21(1), pages 195-206, August.
    2. Dietrich, F.K. & List, C., 2006. "Judgment aggregation on restricted domains," Research Memorandum 033, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    3. Bernard Monjardet & Jean-Pierre Barthélemy & Olivier Hudry & Bruno Leclerc, 2009. "Metric and latticial medians," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00408174, HAL.
    4. Philippe Mongin & Franz Dietrich, 2007. "The Premiss-Based Approach to Logical Aggregation," Working Papers hal-00578986, HAL.
    5. Dietrich, Franz & Mongin, Philippe, 2010. "The premiss-based approach to judgment aggregation," Journal of Economic Theory, Elsevier, vol. 145(2), pages 562-582, March.
    6. Rubinstein, Ariel & Fishburn, Peter C., 1986. "Algebraic aggregation theory," Journal of Economic Theory, Elsevier, vol. 38(1), pages 63-77, February.
    7. Donald J. Brown, 1975. "Aggregation of Preferences," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 89(3), pages 456-469.
    8. Bengt Hansson, 1976. "The existence of group preference functions," Public Choice, Springer, vol. 28(1), pages 89-98, December.
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    Cited by:

    1. Mongin, Philippe & Dietrich, Franz, 2011. "An interpretive account of logical aggregation theory," HEC Research Papers Series 941, HEC Paris.
    2. Philippe Mongin, 2012. "The doctrinal paradox, the discursive dilemma, and logical aggregation theory," Theory and Decision, Springer, vol. 73(3), pages 315-355, September.
    3. Herzberg, Frederik S., 2008. "Judgement aggregation functions and ultraproducts," MPRA Paper 10546, University Library of Munich, Germany, revised 10 Sep 2008.

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    More about this item

    Keywords

    Arrow's theorem; aggregation rule; judgment aggregation; logical connexions; simple game; ultrafilter;
    All these keywords.

    JEL classification:

    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations

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