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Guilbaud's Theorem: an early contribution to judgment aggregation




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

Suggested Citation

  • 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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    References listed on IDEAS

    1. Bonnisseau, Jean-Marc, 1988. "On two existence results of equilibria in economies with increasing returns," Journal of Mathematical Economics, Elsevier, vol. 17(2-3), pages 193-207, April.
    2. Bonnisseau, Jean-Marc, 1992. "Existence of equilibria in the presence of increasing returns : A synthesis," Journal of Mathematical Economics, Elsevier, vol. 21(5), pages 441-452.
    3. Bonnisseau, Jean-Marc & Cornet, Bernard, 1988. "Existence of equilibria when firms follow bounded losses pricing rules," Journal of Mathematical Economics, Elsevier, vol. 17(2-3), pages 119-147, April.
    4. Bonnisseau, Jean-Marc & Cornet, Bernard, 1990. "Existence of Marginal Cost Pricing Equilibria in Economies with Several Nonconvex Firms," Econometrica, Econometric Society, vol. 58(3), pages 661-682, May.
    5. Villar, Antonio, 1994. "Equilibrium with Nonconvex Technologies," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 4(4), pages 629-638, May.
    6. Bonnisseau, Jean-Marc & Cornet, Bernard, 1990. "Existence of Marginal Cost Pricing Equilibria: The Nonsmooth Case," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 31(3), pages 685-708, August.
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    Cited by:

    1. Philippe Mongin & Franz Dietrich, 2011. "An Interpretive Account of Logical Aggregation Theory," Working Papers hal-00625427, HAL.
    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.

    More about this item


    Arrow's theorem; aggregation rule; judgment aggregation; logical connexions; simple game; ultrafilter;

    JEL classification:

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

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