IDEAS home Printed from https://ideas.repec.org/p/mse/cesdoc/10056.html
   My bibliography  Save this paper

Guilbaud's 1952 theorem on the logical problem of aggregation

Author

Listed:

Abstract

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

Suggested Citation

  • 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
    as

    Download full text from publisher

    File URL: http://mse.univ-paris1.fr/pub/mse/CES2010/10056.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    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. Barnett,William A. & Moulin,Hervé & Salles,Maurice & Schofield,Norman J. (ed.), 1995. "Social Choice, Welfare, and Ethics," Cambridge Books, Cambridge University Press, number 9780521443401, September.
    4. 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.
    5. Bengt Hansson, 1976. "The existence of group preference functions," Public Choice, Springer, vol. 28(1), pages 89-98, December.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Bruno Leclerc & Bernard Monjardet, 2010. "Aggregation and residuation," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00504982, HAL.
    2. Olivier Hudry & Bernard Monjardet, 2010. "Consensus theories: An oriented survey," Documents de travail du Centre d'Economie de la Sorbonne 10057, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    3. Susumu Cato, 2022. "Stable preference aggregation with infinite population," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 59(2), pages 287-304, August.
    4. Herzberg, Frederik, 2010. "Judgment aggregators and Boolean algebra homomorphisms," Journal of Mathematical Economics, Elsevier, vol. 46(1), pages 132-140, January.
    5. John Weymark, 1984. "Arrow's theorem with social quasi-orderings," Public Choice, Springer, vol. 42(3), pages 235-246, January.
    6. Gardner Roy, 1979. "Onymous consistent voting systems," CEPREMAP Working Papers (Couverture Orange) 7917, CEPREMAP.
    7. Daniel Eckert & Bernard Monjardet, 2009. "Guilbaud's Theorem : An early contribution to judgment aggregation," Post-Print halshs-00404185, HAL.
    8. Susumu Cato, 2013. "Quasi-decisiveness, quasi-ultrafilter, and social quasi-orderings," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 41(1), pages 169-202, June.
    9. Bossert, Walter & Cato, Susumu, 2020. "Acyclicity, anonymity, and prefilters," Journal of Mathematical Economics, Elsevier, vol. 87(C), pages 134-141.
    10. Susumu Cato, 2018. "Collective rationality and decisiveness coherence," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 50(2), pages 305-328, February.
    11. Cato, Susumu, 2013. "Remarks on Suzumura consistent collective choice rules," Mathematical Social Sciences, Elsevier, vol. 65(1), pages 40-47.
    12. Pierre Batteau, 1978. "Stability of Aggregation Procedures, Ultrafilters and Simple Games," Discussion Papers 318, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    13. Susumu Cato, 2013. "Social choice, the strong Pareto principle, and conditional decisiveness," Theory and Decision, Springer, vol. 75(4), pages 563-579, October.
    14. Susumu Cato, 2012. "Social choice without the Pareto principle: a comprehensive analysis," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 39(4), pages 869-889, October.
    15. Piggins, Ashley & Duddy, Conal, 2016. "Oligarchy and soft incompleteness," MPRA Paper 72392, University Library of Munich, Germany.
    16. Dirk Van de gaer & Michel Martinez & Erik Schokkaert, 1998. "Measuring Intergenerational Mobility and Equality of Opportunity," Working Papers of Department of Economics, Leuven ces9810, KU Leuven, Faculty of Economics and Business (FEB), Department of Economics, Leuven.
    17. Stefan Ambec & Yann Kervinio, 2016. "Cooperative decision-making for the provision of a locally undesirable facility," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 46(1), pages 119-155, January.
    18. Barnett, William A. & Serletis, Apostolos, 2008. "Consumer preferences and demand systems," Journal of Econometrics, Elsevier, vol. 147(2), pages 210-224, December.
    19. Effrosyni Diamantoudi, 2003. "Equilibrium binding agreements under diverse behavioral assumptions," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 22(2), pages 431-446, September.
    20. Boniface Mbih & Issofa Moyouwou & Jérémy Picot, 2008. "Pareto violations of parliamentary voting systems," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 34(2), pages 331-358, February.

    More about this item

    Keywords

    Aggregation; judgment aggregation; logical connectives; simple game; ultrafilter;
    All these keywords.

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:mse:cesdoc:10056. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Lucie Label (email available below). General contact details of provider: https://edirc.repec.org/data/cenp1fr.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.